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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 142912.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142912.bv1 | 142912u1 | \([0, 1, 0, -253, -2423]\) | \(-28094464000/20657483\) | \(-1322078912\) | \([]\) | \(48384\) | \(0.44965\) | \(\Gamma_0(N)\)-optimal |
142912.bv2 | 142912u2 | \([0, 1, 0, 2067, 36785]\) | \(15252992000000/17621717267\) | \(-1127789905088\) | \([]\) | \(145152\) | \(0.99895\) |
Rank
sage: E.rank()
The elliptic curves in class 142912.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 142912.bv do not have complex multiplication.Modular form 142912.2.a.bv
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.