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SageMath
E = EllipticCurve("ia1")
E.isogeny_class()
Elliptic curves in class 283920ia
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
283920.ia4 | 283920ia1 | \([0, 1, 0, 1465, 178608]\) | \(4499456/180075\) | \(-13907002090800\) | \([2]\) | \(589824\) | \(1.2018\) | \(\Gamma_0(N)\)-optimal |
283920.ia3 | 283920ia2 | \([0, 1, 0, -39940, 2927900]\) | \(5702413264/275625\) | \(340579643040000\) | \([2, 2]\) | \(1179648\) | \(1.5484\) | |
283920.ia1 | 283920ia3 | \([0, 1, 0, -631440, 192917700]\) | \(5633270409316/14175\) | \(70062097996800\) | \([2]\) | \(2359296\) | \(1.8949\) | |
283920.ia2 | 283920ia4 | \([0, 1, 0, -110920, -10444732]\) | \(30534944836/8203125\) | \(40545195600000000\) | \([2]\) | \(2359296\) | \(1.8949\) |
Rank
sage: E.rank()
The elliptic curves in class 283920ia have rank \(0\).
Complex multiplication
The elliptic curves in class 283920ia do not have complex multiplication.Modular form 283920.2.a.ia
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.