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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 75504v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75504.bv1 | 75504v1 | \([0, 1, 0, -403, -1564]\) | \(256000/117\) | \(3316362192\) | \([2]\) | \(44800\) | \(0.52177\) | \(\Gamma_0(N)\)-optimal |
75504.bv2 | 75504v2 | \([0, 1, 0, 1412, -10276]\) | \(686000/507\) | \(-229934445312\) | \([2]\) | \(89600\) | \(0.86835\) |
Rank
sage: E.rank()
The elliptic curves in class 75504v have rank \(0\).
Complex multiplication
The elliptic curves in class 75504v do not have complex multiplication.Modular form 75504.2.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 Cremona 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 Cremona labels.