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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9251.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9251.d1 | 9251a3 | \([0, 1, 1, -6576900, -6494214623]\) | \(-52893159101157376/11\) | \(-6543056531\) | \([]\) | \(126000\) | \(2.1804\) | |
9251.d2 | 9251a2 | \([0, 1, 1, -8690, -567683]\) | \(-122023936/161051\) | \(-95796890670371\) | \([]\) | \(25200\) | \(1.3756\) | |
9251.d3 | 9251a1 | \([0, 1, 1, -280, 4197]\) | \(-4096/11\) | \(-6543056531\) | \([]\) | \(5040\) | \(0.57092\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9251.d have rank \(1\).
Complex multiplication
The elliptic curves in class 9251.d do not have complex multiplication.Modular form 9251.2.a.d
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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.