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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 7056.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7056.e1 | 7056be1 | \([0, 0, 0, -73059, -7601566]\) | \(-67645179/8\) | \(-5100326977536\) | \([]\) | \(24192\) | \(1.4639\) | \(\Gamma_0(N)\)-optimal |
| 7056.e2 | 7056be2 | \([0, 0, 0, 9261, -23467374]\) | \(189/512\) | \(-237960855463919616\) | \([]\) | \(72576\) | \(2.0132\) |
Rank
sage: E.rank()
The elliptic curves in class 7056.e have rank \(0\).
Complex multiplication
The elliptic curves in class 7056.e do not have complex multiplication.Modular form 7056.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
