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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 19600.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.bd1 | 19600cj2 | \([0, -1, 0, -986533, -376825063]\) | \(-225637236736/1715\) | \(-807072140000000\) | \([]\) | \(165888\) | \(2.0352\) | |
19600.bd2 | 19600cj1 | \([0, -1, 0, -6533, -995063]\) | \(-65536/875\) | \(-411771500000000\) | \([]\) | \(55296\) | \(1.4859\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 19600.bd do not have complex multiplication.Modular form 19600.2.a.bd
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.