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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 418950j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.j2 | 418950j1 | \([1, -1, 0, 104508, 20185416]\) | \(76895/152\) | \(-249525808284375000\) | \([]\) | \(7484400\) | \(2.0227\) | \(\Gamma_0(N)\)-optimal* |
418950.j1 | 418950j2 | \([1, -1, 0, -3754242, 2810061666]\) | \(-3564664705/13718\) | \(-22519704197664843750\) | \([3]\) | \(22453200\) | \(2.5720\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 418950j have rank \(0\).
Complex multiplication
The elliptic curves in class 418950j do not have complex multiplication.Modular form 418950.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.