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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 6800.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6800.s1 | 6800s1 | \([0, 1, 0, -1008, -52012]\) | \(-1771561/17000\) | \(-1088000000000\) | \([]\) | \(6912\) | \(0.99196\) | \(\Gamma_0(N)\)-optimal |
| 6800.s2 | 6800s2 | \([0, 1, 0, 8992, 1327988]\) | \(1256216039/12577280\) | \(-804945920000000\) | \([]\) | \(20736\) | \(1.5413\) |
Rank
sage: E.rank()
The elliptic curves in class 6800.s have rank \(1\).
Complex multiplication
The elliptic curves in class 6800.s do not have complex multiplication.Modular form 6800.2.a.s
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.
