Properties

 Label 179520.gd Number of curves $8$ Conductor $179520$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("gd1")

sage: E.isogeny_class()

Elliptic curves in class 179520.gd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179520.gd1 179520bv7 $$[0, 1, 0, -12879134881, 562567756120799]$$ $$901247067798311192691198986281/552431869440$$ $$144816699982479360$$ $$[2]$$ $$127401984$$ $$4.0005$$
179520.gd2 179520bv8 $$[0, 1, 0, -810352801, 8665841992415]$$ $$224494757451893010998773801/6152490825146276160000$$ $$1612838554867145417687040000$$ $$[2]$$ $$127401984$$ $$4.0005$$
179520.gd3 179520bv6 $$[0, 1, 0, -804946081, 8789916484319]$$ $$220031146443748723000125481/172266701724057600$$ $$45158682256751355494400$$ $$[2, 2]$$ $$63700992$$ $$3.6539$$
179520.gd4 179520bv4 $$[0, 1, 0, -159034081, 771320361119]$$ $$1696892787277117093383481/1440538624914939000$$ $$377628557289701769216000$$ $$[2]$$ $$42467328$$ $$3.4512$$
179520.gd5 179520bv5 $$[0, 1, 0, -104152801, -404787487585]$$ $$476646772170172569823801/5862293314453125000$$ $$1536765018624000000000000$$ $$[2]$$ $$42467328$$ $$3.4512$$
179520.gd6 179520bv3 $$[0, 1, 0, -49971361, 139265147615]$$ $$-52643812360427830814761/1504091705903677440$$ $$-394288616152413618831360$$ $$[2]$$ $$31850496$$ $$3.3074$$
179520.gd7 179520bv2 $$[0, 1, 0, -12154081, 6281193119]$$ $$757443433548897303481/373234243041000000$$ $$97841117407739904000000$$ $$[2, 2]$$ $$21233664$$ $$3.1046$$
179520.gd8 179520bv1 $$[0, 1, 0, 2775839, 754136735]$$ $$9023321954633914439/6156756739584000$$ $$-1613956838741508096000$$ $$[2]$$ $$10616832$$ $$2.7581$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 179520.gd have rank $$0$$.

Complex multiplication

The elliptic curves in class 179520.gd do not have complex multiplication.

Modular form 179520.2.a.gd

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 4 q^{7} + q^{9} + q^{11} - 2 q^{13} - q^{15} - q^{17} - 4 q^{19} + O(q^{20})$$

Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.