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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 47610.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.l1 | 47610p2 | \([1, -1, 0, -22455, -2622699]\) | \(-3247061909089/5859375000\) | \(-2259615234375000\) | \([]\) | \(331776\) | \(1.6363\) | |
47610.l2 | 47610p1 | \([1, -1, 0, 2385, 74925]\) | \(3889584671/8640000\) | \(-3331938240000\) | \([]\) | \(110592\) | \(1.0870\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47610.l have rank \(1\).
Complex multiplication
The elliptic curves in class 47610.l do not have complex multiplication.Modular form 47610.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.