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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 93925a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 93925.l2 | 93925a1 | \([0, 1, 1, -963, 10369]\) | \(163840/13\) | \(7844709925\) | \([]\) | \(55296\) | \(0.64218\) | \(\Gamma_0(N)\)-optimal |
| 93925.l1 | 93925a2 | \([0, 1, 1, -15413, -739586]\) | \(671088640/2197\) | \(1325755977325\) | \([]\) | \(165888\) | \(1.1915\) |
Rank
sage: E.rank()
The elliptic curves in class 93925a have rank \(1\).
Complex multiplication
The elliptic curves in class 93925a do not have complex multiplication.Modular form 93925.2.a.a
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 Cremona 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 Cremona labels.
