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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 122304ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122304.c2 | 122304ci1 | \([0, -1, 0, -1045, -11339]\) | \(1048576/117\) | \(14095291392\) | \([2]\) | \(138240\) | \(0.68043\) | \(\Gamma_0(N)\)-optimal |
| 122304.c1 | 122304ci2 | \([0, -1, 0, -3985, 85681]\) | \(3631696/507\) | \(977273536512\) | \([2]\) | \(276480\) | \(1.0270\) |
Rank
sage: E.rank()
The elliptic curves in class 122304ci have rank \(1\).
Complex multiplication
The elliptic curves in class 122304ci do not have complex multiplication.Modular form 122304.2.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.
