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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 3042.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3042.l1 | 3042k2 | \([1, -1, 1, -323498, 77783203]\) | \(-1064019559329/125497034\) | \(-441591905411504874\) | \([]\) | \(32928\) | \(2.1216\) | |
| 3042.l2 | 3042k1 | \([1, -1, 1, -4088, -152837]\) | \(-2146689/1664\) | \(-5855189618304\) | \([]\) | \(4704\) | \(1.1486\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3042.l have rank \(1\).
Complex multiplication
The elliptic curves in class 3042.l do not have complex multiplication.Modular form 3042.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
