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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 118580.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 118580.l1 | 118580z2 | \([0, -1, 0, -2587020, 1603022632]\) | \(-296587984/125\) | \(-807011455704608000\) | \([]\) | \(1796256\) | \(2.3972\) | |
| 118580.l2 | 118580z1 | \([0, -1, 0, 21740, 8548520]\) | \(176/5\) | \(-32280458228184320\) | \([]\) | \(598752\) | \(1.8478\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 118580.l have rank \(1\).
Complex multiplication
The elliptic curves in class 118580.l do not have complex multiplication.Modular form 118580.2.a.l
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.
