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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 102850.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102850.p1 | 102850q1 | \([1, 1, 0, -682200, -377463500]\) | \(-2029568425/2377892\) | \(-41138483685664062500\) | \([]\) | \(2073600\) | \(2.4577\) | \(\Gamma_0(N)\)-optimal |
| 102850.p2 | 102850q2 | \([1, 1, 0, 5745925, 7008452125]\) | \(1212683025575/1927458368\) | \(-33345801502660625000000\) | \([]\) | \(6220800\) | \(3.0070\) |
Rank
sage: E.rank()
The elliptic curves in class 102850.p have rank \(1\).
Complex multiplication
The elliptic curves in class 102850.p do not have complex multiplication.Modular form 102850.2.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.
