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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 350658.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350658.w1 | 350658w4 | \([1, -1, 0, -1651458177, -25705822455747]\) | \(385693937170561837203625/2159357734550274048\) | \(2788741347784083553163968512\) | \([2]\) | \(248832000\) | \(4.1086\) | |
| 350658.w2 | 350658w2 | \([1, -1, 0, -121963122, 493976764980]\) | \(155355156733986861625/8291568305839392\) | \(10708294879767170426434848\) | \([2]\) | \(82944000\) | \(3.5593\) | |
| 350658.w3 | 350658w3 | \([1, -1, 0, -45662337, -847139375043]\) | \(-8152944444844179625/235342826399858688\) | \(-303937722029345081678364672\) | \([2]\) | \(124416000\) | \(3.7620\) | |
| 350658.w4 | 350658w1 | \([1, -1, 0, 5057838, 30832940628]\) | \(11079872671250375/324440155855872\) | \(-419004069145226468563968\) | \([2]\) | \(41472000\) | \(3.2127\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 350658.w have rank \(1\).
Complex multiplication
The elliptic curves in class 350658.w do not have complex multiplication.Modular form 350658.2.a.w
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.
