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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 95370h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 95370.f3 | 95370h1 | \([1, 1, 0, -12686383, 29430532837]\) | \(-9354997870579612441/10093752054144000\) | \(-243638636675792535936000\) | \([2]\) | \(13271040\) | \(3.1824\) | \(\Gamma_0(N)\)-optimal |
| 95370.f2 | 95370h2 | \([1, 1, 0, -239863503, 1429250510853]\) | \(63229930193881628103961/26218934428500000\) | \(632861338874394316500000\) | \([2]\) | \(26542080\) | \(3.5290\) | |
| 95370.f4 | 95370h3 | \([1, 1, 0, 106331042, -531588793868]\) | \(5508208700580085578359/8246033269590589440\) | \(-199039197021038454358671360\) | \([2]\) | \(39813120\) | \(3.7317\) | |
| 95370.f1 | 95370h4 | \([1, 1, 0, -698614878, -5342106600972]\) | \(1562225332123379392365961/393363080510106009600\) | \(9494828497865239004034662400\) | \([2]\) | \(79626240\) | \(4.0783\) |
Rank
sage: E.rank()
The elliptic curves in class 95370h have rank \(2\).
Complex multiplication
The elliptic curves in class 95370h do not have complex multiplication.Modular form 95370.2.a.h
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
