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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 463680.eq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.eq1 | 463680eq1 | \([0, 0, 0, -93708, -11037168]\) | \(476196576129/197225\) | \(37690284441600\) | \([2]\) | \(2359296\) | \(1.5670\) | \(\Gamma_0(N)\)-optimal |
463680.eq2 | 463680eq2 | \([0, 0, 0, -79308, -14545008]\) | \(-288673724529/311181605\) | \(-59467730791956480\) | \([2]\) | \(4718592\) | \(1.9136\) |
Rank
sage: E.rank()
The elliptic curves in class 463680.eq have rank \(1\).
Complex multiplication
The elliptic curves in class 463680.eq do not have complex multiplication.Modular form 463680.2.a.eq
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.