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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 29008a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29008.i1 | 29008a1 | \([0, 0, 0, -490, 3087]\) | \(6912000/1813\) | \(3412762192\) | \([2]\) | \(10752\) | \(0.53804\) | \(\Gamma_0(N)\)-optimal |
| 29008.i2 | 29008a2 | \([0, 0, 0, 1225, 19894]\) | \(6750000/9583\) | \(-288622173952\) | \([2]\) | \(21504\) | \(0.88462\) |
Rank
sage: E.rank()
The elliptic curves in class 29008a have rank \(0\).
Complex multiplication
The elliptic curves in class 29008a do not have complex multiplication.Modular form 29008.2.a.a
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.
