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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 104104q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104104.v2 | 104104q1 | \([0, -1, 0, 646876, 212067140]\) | \(24226243449392/29774625727\) | \(-36791406446263076608\) | \([2]\) | \(2257920\) | \(2.4404\) | \(\Gamma_0(N)\)-optimal |
| 104104.v1 | 104104q2 | \([0, -1, 0, -3851904, 2042170844]\) | \(1278763167594532/375974556419\) | \(1858311549638898658304\) | \([2]\) | \(4515840\) | \(2.7870\) |
Rank
sage: E.rank()
The elliptic curves in class 104104q have rank \(1\).
Complex multiplication
The elliptic curves in class 104104q do not have complex multiplication.Modular form 104104.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
