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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 177450.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177450.bh1 | 177450ke2 | \([1, 1, 0, -270824375, -1715569453125]\) | \(63993649810037164314733/273488906250\) | \(9388361359863281250\) | \([2]\) | \(34836480\) | \(3.2706\) | |
177450.bh2 | 177450ke1 | \([1, 1, 0, -16918125, -26838984375]\) | \(-15600206875151814733/32299804687500\) | \(-1108791732788085937500\) | \([2]\) | \(17418240\) | \(2.9241\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 177450.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 177450.bh do not have complex multiplication.Modular form 177450.2.a.bh
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.