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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 155526.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155526.g1 | 155526cx4 | \([1, 1, 0, -39308950790, -2985222251331564]\) | \(385693937170561837203625/2159357734550274048\) | \(37607966627466733681243275952128\) | \([2]\) | \(729907200\) | \(4.9011\) | |
| 155526.g2 | 155526cx2 | \([1, 1, 0, -2903035895, 57359633018997]\) | \(155355156733986861625/8291568305839392\) | \(144408228032819613182494823712\) | \([2]\) | \(243302400\) | \(4.3518\) | |
| 155526.g3 | 155526cx3 | \([1, 1, 0, -1086881030, -98378122084332]\) | \(-8152944444844179625/235342826399858688\) | \(-4098795220284756153215817351168\) | \([2]\) | \(364953600\) | \(4.5545\) | |
| 155526.g4 | 155526cx1 | \([1, 1, 0, 120389545, 3580755347541]\) | \(11079872671250375/324440155855872\) | \(-5650538749930165630890580992\) | \([2]\) | \(121651200\) | \(4.0052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155526.g have rank \(1\).
Complex multiplication
The elliptic curves in class 155526.g do not have complex multiplication.Modular form 155526.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
