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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 62400b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.cq3 | 62400b1 | \([0, -1, 0, -21633, 1195137]\) | \(273359449/9360\) | \(38338560000000\) | \([2]\) | \(147456\) | \(1.3783\) | \(\Gamma_0(N)\)-optimal |
62400.cq2 | 62400b2 | \([0, -1, 0, -53633, -3124863]\) | \(4165509529/1368900\) | \(5607014400000000\) | \([2, 2]\) | \(294912\) | \(1.7249\) | |
62400.cq4 | 62400b3 | \([0, -1, 0, 154367, -21636863]\) | \(99317171591/106616250\) | \(-436700160000000000\) | \([2]\) | \(589824\) | \(2.0715\) | |
62400.cq1 | 62400b4 | \([0, -1, 0, -773633, -261604863]\) | \(12501706118329/2570490\) | \(10528727040000000\) | \([2]\) | \(589824\) | \(2.0715\) |
Rank
sage: E.rank()
The elliptic curves in class 62400b have rank \(1\).
Complex multiplication
The elliptic curves in class 62400b do not have complex multiplication.Modular form 62400.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.