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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 9800.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9800.bj1 | 9800bg2 | \([0, -1, 0, -49408, 4192812]\) | \(3543122/49\) | \(184473632000000\) | \([2]\) | \(30720\) | \(1.5430\) | |
| 9800.bj2 | 9800bg1 | \([0, -1, 0, -408, 174812]\) | \(-4/7\) | \(-13176688000000\) | \([2]\) | \(15360\) | \(1.1964\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9800.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 9800.bj do not have complex multiplication.Modular form 9800.2.a.bj
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.
