Properties

 Label 81120.bw Number of curves $4$ Conductor $81120$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

Elliptic curves in class 81120.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81120.bw1 81120u4 $$[0, 1, 0, -175985, -28474497]$$ $$30488290624/195$$ $$3855268884480$$ $$$$ $$258048$$ $$1.5997$$
81120.bw2 81120u3 $$[0, 1, 0, -36560, 2176188]$$ $$2186875592/428415$$ $$1058753217400320$$ $$$$ $$258048$$ $$1.5997$$
81120.bw3 81120u1 $$[0, 1, 0, -11210, -429792]$$ $$504358336/38025$$ $$11746522382400$$ $$[2, 2]$$ $$129024$$ $$1.2531$$ $$\Gamma_0(N)$$-optimal
81120.bw4 81120u2 $$[0, 1, 0, 10760, -1888600]$$ $$55742968/658125$$ $$-1626441560640000$$ $$$$ $$258048$$ $$1.5997$$

Rank

sage: E.rank()

The elliptic curves in class 81120.bw have rank $$1$$.

Complex multiplication

The elliptic curves in class 81120.bw do not have complex multiplication.

Modular form 81120.2.a.bw

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 