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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 212415.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212415.v1 | 212415s2 | \([1, 0, 0, -10291, 195446]\) | \(208527857/91875\) | \(53104626211875\) | \([2]\) | \(589824\) | \(1.3294\) | |
212415.v2 | 212415s1 | \([1, 0, 0, 2204, 23015]\) | \(2048383/1575\) | \(-910365020775\) | \([2]\) | \(294912\) | \(0.98283\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212415.v have rank \(1\).
Complex multiplication
The elliptic curves in class 212415.v do not have complex multiplication.Modular form 212415.2.a.v
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.