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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 54096.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54096.b1 | 54096i2 | \([0, -1, 0, -2760, -50784]\) | \(19307236/1587\) | \(191189978112\) | \([2]\) | \(92160\) | \(0.90718\) | |
54096.b2 | 54096i1 | \([0, -1, 0, 180, -3744]\) | \(21296/207\) | \(-6234455808\) | \([2]\) | \(46080\) | \(0.56061\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54096.b have rank \(0\).
Complex multiplication
The elliptic curves in class 54096.b do not have complex multiplication.Modular form 54096.2.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 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.