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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 261072.ea
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 261072.ea1 | 261072ea1 | \([0, 0, 0, -4410, -83349]\) | \(6912000/1813\) | \(2487903637968\) | \([2]\) | \(344064\) | \(1.0873\) | \(\Gamma_0(N)\)-optimal |
| 261072.ea2 | 261072ea2 | \([0, 0, 0, 11025, -537138]\) | \(6750000/9583\) | \(-210405564811008\) | \([2]\) | \(688128\) | \(1.4339\) |
Rank
sage: E.rank()
The elliptic curves in class 261072.ea have rank \(1\).
Complex multiplication
The elliptic curves in class 261072.ea do not have complex multiplication.Modular form 261072.2.a.ea
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
