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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 377520.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.p1 | 377520p2 | \([0, -1, 0, -1068746576, -13447779023424]\) | \(-18605093748570727251049/91759078125000\) | \(-665832670012224000000000\) | \([]\) | \(130636800\) | \(3.7707\) | |
| 377520.p2 | 377520p1 | \([0, -1, 0, -7886336, -33392760960]\) | \(-7475384530020889/62069784455250\) | \(-450397836981563986944000\) | \([]\) | \(43545600\) | \(3.2214\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.p have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.p do not have complex multiplication.Modular form 377520.2.a.p
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.
