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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 405720.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405720.bv1 | 405720bv4 | \([0, 0, 0, -952637763, -11317220915938]\) | \(544328872410114151778/14166950625\) | \(2488410934281780480000\) | \([2]\) | \(75497472\) | \(3.6208\) | |
405720.bv2 | 405720bv3 | \([0, 0, 0, -92476083, 39725788718]\) | \(497927680189263938/284271240234375\) | \(49931963569687500000000000\) | \([2]\) | \(75497472\) | \(3.6208\) | \(\Gamma_0(N)\)-optimal* |
405720.bv3 | 405720bv2 | \([0, 0, 0, -59612763, -176376830938]\) | \(266763091319403556/1355769140625\) | \(119069757606819600000000\) | \([2, 2]\) | \(37748736\) | \(3.2743\) | \(\Gamma_0(N)\)-optimal* |
405720.bv4 | 405720bv1 | \([0, 0, 0, -1744743, -5677745542]\) | \(-26752376766544/618796614375\) | \(-13586377037536406880000\) | \([2]\) | \(18874368\) | \(2.9277\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 405720.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 405720.bv do not have complex multiplication.Modular form 405720.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.