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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 131648k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 131648.p1 | 131648k1 | \([0, 1, 0, -2097, 14287]\) | \(35152/17\) | \(493429342208\) | \([2]\) | \(138240\) | \(0.93732\) | \(\Gamma_0(N)\)-optimal |
| 131648.p2 | 131648k2 | \([0, 1, 0, 7583, 116895]\) | \(415292/289\) | \(-33553195270144\) | \([2]\) | \(276480\) | \(1.2839\) |
Rank
sage: E.rank()
The elliptic curves in class 131648k have rank \(1\).
Complex multiplication
The elliptic curves in class 131648k do not have complex multiplication.Modular form 131648.2.a.k
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.
