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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 19600.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.ba1 | 19600cw2 | \([0, 1, 0, -476408, -126720812]\) | \(544737993463/20000\) | \(439040000000000\) | \([2]\) | \(184320\) | \(1.8972\) | |
19600.ba2 | 19600cw1 | \([0, 1, 0, -28408, -2176812]\) | \(-115501303/25600\) | \(-561971200000000\) | \([2]\) | \(92160\) | \(1.5507\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 19600.ba do not have complex multiplication.Modular form 19600.2.a.ba
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.