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SageMath
E = EllipticCurve("lv1")
E.isogeny_class()
Elliptic curves in class 342720.lv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
342720.lv1 | 342720lv2 | \([0, 0, 0, -31131372, 63746061136]\) | \(17460273607244690041/918397653311250\) | \(175508524699196129280000\) | \([2]\) | \(47185920\) | \(3.2172\) | |
342720.lv2 | 342720lv1 | \([0, 0, 0, 1268628, 3961581136]\) | \(1181569139409959/36161310937500\) | \(-6910534136217600000000\) | \([2]\) | \(23592960\) | \(2.8706\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 342720.lv have rank \(0\).
Complex multiplication
The elliptic curves in class 342720.lv do not have complex multiplication.Modular form 342720.2.a.lv
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.