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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 19600.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.p1 | 19600bw2 | \([0, 1, 0, -3107008, 3659399988]\) | \(-8990558521/10485760\) | \(-3868692462960640000000\) | \([]\) | \(1016064\) | \(2.8363\) | |
| 19600.p2 | 19600bw1 | \([0, 1, 0, 322992, -93020012]\) | \(10100279/16000\) | \(-5903156224000000000\) | \([]\) | \(338688\) | \(2.2870\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.p have rank \(0\).
Complex multiplication
The elliptic curves in class 19600.p do not have complex multiplication.Modular form 19600.2.a.p
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.
