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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 75600.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75600.gb1 | 75600dg2 | \([0, 0, 0, -424875, -106595750]\) | \(-545407363875/14\) | \(-217728000000\) | \([]\) | \(373248\) | \(1.6917\) | |
| 75600.gb2 | 75600dg1 | \([0, 0, 0, -4875, -167750]\) | \(-7414875/2744\) | \(-4741632000000\) | \([]\) | \(124416\) | \(1.1424\) | \(\Gamma_0(N)\)-optimal |
| 75600.gb3 | 75600dg3 | \([0, 0, 0, 37125, 1694250]\) | \(4492125/3584\) | \(-4514807808000000\) | \([]\) | \(373248\) | \(1.6917\) |
Rank
sage: E.rank()
The elliptic curves in class 75600.gb have rank \(1\).
Complex multiplication
The elliptic curves in class 75600.gb do not have complex multiplication.Modular form 75600.2.a.gb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
