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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 3025.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3025.e1 | 3025c2 | \([1, 0, 1, -7626, 1001273]\) | \(-121\) | \(-405272259390625\) | \([]\) | \(9240\) | \(1.4857\) | |
3025.e2 | 3025c1 | \([1, 0, 1, -751, -7977]\) | \(-24729001\) | \(-1890625\) | \([]\) | \(840\) | \(0.28676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3025.e have rank \(0\).
Complex multiplication
The elliptic curves in class 3025.e do not have complex multiplication.Modular form 3025.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.