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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 31200.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 31200.cb1 | 31200n4 | \([0, 1, 0, -93608, -11054712]\) | \(11339065490696/351\) | \(2808000000\) | \([2]\) | \(98304\) | \(1.3174\) | |
| 31200.cb2 | 31200n3 | \([0, 1, 0, -9233, 45663]\) | \(1360251712/771147\) | \(49353408000000\) | \([2]\) | \(98304\) | \(1.3174\) | |
| 31200.cb3 | 31200n1 | \([0, 1, 0, -5858, -173712]\) | \(22235451328/123201\) | \(123201000000\) | \([2, 2]\) | \(49152\) | \(0.97086\) | \(\Gamma_0(N)\)-optimal |
| 31200.cb4 | 31200n2 | \([0, 1, 0, -2608, -362212]\) | \(-245314376/6908733\) | \(-55269864000000\) | \([2]\) | \(98304\) | \(1.3174\) |
Rank
sage: E.rank()
The elliptic curves in class 31200.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 31200.cb do not have complex multiplication.Modular form 31200.2.a.cb
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.
