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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2793.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2793.i1 | 2793c3 | \([1, 1, 0, -4974, -137115]\) | \(115714886617/1539\) | \(181061811\) | \([2]\) | \(2304\) | \(0.72795\) | |
2793.i2 | 2793c2 | \([1, 1, 0, -319, -2120]\) | \(30664297/3249\) | \(382241601\) | \([2, 2]\) | \(1152\) | \(0.38137\) | |
2793.i3 | 2793c1 | \([1, 1, 0, -74, 183]\) | \(389017/57\) | \(6705993\) | \([2]\) | \(576\) | \(0.034799\) | \(\Gamma_0(N)\)-optimal |
2793.i4 | 2793c4 | \([1, 1, 0, 416, -9617]\) | \(67419143/390963\) | \(-45996405987\) | \([2]\) | \(2304\) | \(0.72795\) |
Rank
sage: E.rank()
The elliptic curves in class 2793.i have rank \(1\).
Complex multiplication
The elliptic curves in class 2793.i do not have complex multiplication.Modular form 2793.2.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 LMFDB 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 LMFDB labels.