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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 10304.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10304.v1 | 10304l2 | \([0, 0, 0, -15244, 722160]\) | \(1494447319737/5411854\) | \(1418685054976\) | \([2]\) | \(18432\) | \(1.1927\) | |
10304.v2 | 10304l1 | \([0, 0, 0, -524, 21488]\) | \(-60698457/725788\) | \(-190260969472\) | \([2]\) | \(9216\) | \(0.84615\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10304.v have rank \(1\).
Complex multiplication
The elliptic curves in class 10304.v do not have complex multiplication.Modular form 10304.2.a.v
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.