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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 38720ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.g2 | 38720ci1 | \([0, 1, 0, -1976, 32074]\) | \(7529536/275\) | \(31179473600\) | \([2]\) | \(46080\) | \(0.78318\) | \(\Gamma_0(N)\)-optimal |
| 38720.g1 | 38720ci2 | \([0, 1, 0, -5001, -93161]\) | \(1906624/605\) | \(4390069882880\) | \([2]\) | \(92160\) | \(1.1297\) |
Rank
sage: E.rank()
The elliptic curves in class 38720ci have rank \(1\).
Complex multiplication
The elliptic curves in class 38720ci do not have complex multiplication.Modular form 38720.2.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 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.
