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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 66640ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66640.bj1 | 66640ca1 | \([0, 0, 0, -1372, 19551]\) | \(151732224/85\) | \(160002640\) | \([2]\) | \(27648\) | \(0.52141\) | \(\Gamma_0(N)\)-optimal |
| 66640.bj2 | 66640ca2 | \([0, 0, 0, -1127, 26754]\) | \(-5256144/7225\) | \(-217603590400\) | \([2]\) | \(55296\) | \(0.86798\) |
Rank
sage: E.rank()
The elliptic curves in class 66640ca have rank \(0\).
Complex multiplication
The elliptic curves in class 66640ca do not have complex multiplication.Modular form 66640.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
