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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 350658ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.ca2 | 350658ca1 | \([1, -1, 0, -137418, 26367732]\) | \(-5999796014211/2790817792\) | \(-133490806877159424\) | \([]\) | \(5702400\) | \(1.9923\) | \(\Gamma_0(N)\)-optimal |
| 350658.ca1 | 350658ca2 | \([1, -1, 0, -12159978, 16324061012]\) | \(-5702623460245179/252448\) | \(-8802769657629024\) | \([]\) | \(17107200\) | \(2.5416\) |
Rank
sage: E.rank()
The elliptic curves in class 350658ca have rank \(1\).
Complex multiplication
The elliptic curves in class 350658ca do not have complex multiplication.Modular form 350658.2.a.ca
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.
