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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 103056l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103056.k2 | 103056l1 | \([0, -1, 0, -18741768, -31220491536]\) | \(177744208950637895247625/17681950027579392\) | \(72425267312965189632\) | \([]\) | \(4872960\) | \(2.8453\) | \(\Gamma_0(N)\)-optimal |
| 103056.k1 | 103056l2 | \([0, -1, 0, -40464888, 53255791728]\) | \(1788952473315990499029625/736296634487918297088\) | \(3015871014862513344872448\) | \([]\) | \(14618880\) | \(3.3946\) |
Rank
sage: E.rank()
The elliptic curves in class 103056l have rank \(1\).
Complex multiplication
The elliptic curves in class 103056l do not have complex multiplication.Modular form 103056.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
