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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 397800i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 397800.i2 | 397800i1 | \([0, 0, 0, -14734875, 21598843750]\) | \(242664113947028/2205421101\) | \(3215503965258000000000\) | \([2]\) | \(25804800\) | \(2.9492\) | \(\Gamma_0(N)\)-optimal |
| 397800.i1 | 397800i2 | \([0, 0, 0, -25669875, -14760031250]\) | \(641515943191354/338972315643\) | \(988443272414988000000000\) | \([2]\) | \(51609600\) | \(3.2957\) |
Rank
sage: E.rank()
The elliptic curves in class 397800i have rank \(0\).
Complex multiplication
The elliptic curves in class 397800i do not have complex multiplication.Modular form 397800.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
