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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 48960.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48960.ci1 | 48960do2 | \([0, 0, 0, -85117068, -302252938992]\) | \(13217291350697580147/90312500000\) | \(465992663040000000000\) | \([2]\) | \(3686400\) | \(3.1468\) | |
| 48960.ci2 | 48960do1 | \([0, 0, 0, -5214348, -4918937328]\) | \(-3038732943445107/267267200000\) | \(-1379040047294054400000\) | \([2]\) | \(1843200\) | \(2.8002\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48960.ci have rank \(1\).
Complex multiplication
The elliptic curves in class 48960.ci do not have complex multiplication.Modular form 48960.2.a.ci
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.
