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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 235950.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.v1 | 235950v2 | \([1, 1, 0, -1669916525, 26265193405125]\) | \(-18605093748570727251049/91759078125000\) | \(-2539950065659423828125000\) | \([]\) | \(130636800\) | \(3.8823\) | |
235950.v2 | 235950v1 | \([1, 1, 0, -12322400, 65220236250]\) | \(-7475384530020889/62069784455250\) | \(-1718131397176986644531250\) | \([]\) | \(43545600\) | \(3.3330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.v have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.v do not have complex multiplication.Modular form 235950.2.a.v
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.