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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 370881p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 370881.p2 | 370881p1 | \([0, 0, 1, -70644, 7127685]\) | \(1835008/29\) | \(616182831633789\) | \([]\) | \(1693440\) | \(1.6383\) | \(\Gamma_0(N)\)-optimal |
| 370881.p1 | 370881p2 | \([0, 0, 1, -600474, -175716648]\) | \(1126924288/24389\) | \(518209761404016549\) | \([]\) | \(5080320\) | \(2.1876\) |
Rank
sage: E.rank()
The elliptic curves in class 370881p have rank \(1\).
Complex multiplication
The elliptic curves in class 370881p do not have complex multiplication.Modular form 370881.2.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 Cremona 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 Cremona labels.
