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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2394.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2394.e1 | 2394e1 | \([1, -1, 0, -3186, 56020]\) | \(4906933498657/1032471552\) | \(752671761408\) | \([2]\) | \(3840\) | \(0.99363\) | \(\Gamma_0(N)\)-optimal |
| 2394.e2 | 2394e2 | \([1, -1, 0, 6894, 332212]\) | \(49702082429663/94844496096\) | \(-69141637653984\) | \([2]\) | \(7680\) | \(1.3402\) |
Rank
sage: E.rank()
The elliptic curves in class 2394.e have rank \(1\).
Complex multiplication
The elliptic curves in class 2394.e do not have complex multiplication.Modular form 2394.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
