Properties

 Label 129360.ct Number of curves $4$ Conductor $129360$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

Elliptic curves in class 129360.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.ct1 129360bj4 $$[0, -1, 0, -1459040, 678717600]$$ $$1425631925916578/270703125$$ $$65224605600000000$$ $$[4]$$ $$1572864$$ $$2.2275$$
129360.ct2 129360bj3 $$[0, -1, 0, -639760, -190512608]$$ $$120186986927618/4332064275$$ $$1043789885213644800$$ $$[2]$$ $$1572864$$ $$2.2275$$
129360.ct3 129360bj2 $$[0, -1, 0, -100760, 8270592]$$ $$939083699236/300155625$$ $$36160521344640000$$ $$[2, 2]$$ $$786432$$ $$1.8809$$
129360.ct4 129360bj1 $$[0, -1, 0, 17820, 871200]$$ $$20777545136/23059575$$ $$-694511600428800$$ $$[2]$$ $$393216$$ $$1.5344$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 129360.ct have rank $$1$$.

Complex multiplication

The elliptic curves in class 129360.ct do not have complex multiplication.

Modular form 129360.2.a.ct

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.