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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 50400dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50400.ef3 | 50400dv1 | \([0, 0, 0, -3225, 65000]\) | \(5088448/441\) | \(321489000000\) | \([2, 2]\) | \(65536\) | \(0.94882\) | \(\Gamma_0(N)\)-optimal |
50400.ef4 | 50400dv2 | \([0, 0, 0, 3525, 301250]\) | \(830584/7203\) | \(-42007896000000\) | \([2]\) | \(131072\) | \(1.2954\) | |
50400.ef2 | 50400dv3 | \([0, 0, 0, -11100, -376000]\) | \(3241792/567\) | \(26453952000000\) | \([2]\) | \(131072\) | \(1.2954\) | |
50400.ef1 | 50400dv4 | \([0, 0, 0, -50475, 4364750]\) | \(2438569736/21\) | \(122472000000\) | \([2]\) | \(131072\) | \(1.2954\) |
Rank
sage: E.rank()
The elliptic curves in class 50400dv have rank \(0\).
Complex multiplication
The elliptic curves in class 50400dv do not have complex multiplication.Modular form 50400.2.a.dv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.