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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3042.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3042.k1 | 3042l2 | \([1, -1, 1, -3503, 80695]\) | \(-38575685889/16384\) | \(-2018525184\) | \([]\) | \(2688\) | \(0.74623\) | |
| 3042.k2 | 3042l1 | \([1, -1, 1, 7, -35]\) | \(351/4\) | \(-492804\) | \([]\) | \(384\) | \(-0.22672\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3042.k have rank \(1\).
Complex multiplication
The elliptic curves in class 3042.k do not have complex multiplication.Modular form 3042.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
