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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 79200.ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79200.ci1 | 79200w4 | \([0, 0, 0, -119100, 15820000]\) | \(4004529472/99\) | \(4618944000000\) | \([2]\) | \(262144\) | \(1.5392\) | |
| 79200.ci2 | 79200w3 | \([0, 0, 0, -32475, -2024750]\) | \(649461896/72171\) | \(420901272000000\) | \([2]\) | \(262144\) | \(1.5392\) | |
| 79200.ci3 | 79200w1 | \([0, 0, 0, -7725, 227500]\) | \(69934528/9801\) | \(7144929000000\) | \([2, 2]\) | \(131072\) | \(1.1927\) | \(\Gamma_0(N)\)-optimal |
| 79200.ci4 | 79200w2 | \([0, 0, 0, 12525, 1219750]\) | \(37259704/131769\) | \(-768476808000000\) | \([2]\) | \(262144\) | \(1.5392\) |
Rank
sage: E.rank()
The elliptic curves in class 79200.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 79200.ci do not have complex multiplication.Modular form 79200.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
