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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9282.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9282.j1 | 9282m3 | \([1, 0, 1, -16502, -817270]\) | \(496930471478093017/250614\) | \(250614\) | \([2]\) | \(10752\) | \(0.80496\) | |
| 9282.j2 | 9282m4 | \([1, 0, 1, -1242, -7286]\) | \(211634149400857/100188617802\) | \(100188617802\) | \([2]\) | \(10752\) | \(0.80496\) | |
| 9282.j3 | 9282m2 | \([1, 0, 1, -1032, -12830]\) | \(121382959848697/86155524\) | \(86155524\) | \([2, 2]\) | \(5376\) | \(0.45838\) | |
| 9282.j4 | 9282m1 | \([1, 0, 1, -52, -286]\) | \(-15124197817/25469808\) | \(-25469808\) | \([2]\) | \(2688\) | \(0.11181\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9282.j have rank \(0\).
Complex multiplication
The elliptic curves in class 9282.j do not have complex multiplication.Modular form 9282.2.a.j
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.
