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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 117600.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.bf1 | 117600es1 | \([0, -1, 0, -32258, -2186988]\) | \(31554496/525\) | \(61765725000000\) | \([2]\) | \(442368\) | \(1.4447\) | \(\Gamma_0(N)\)-optimal |
| 117600.bf2 | 117600es2 | \([0, -1, 0, -1633, -6198863]\) | \(-64/2205\) | \(-16602626880000000\) | \([2]\) | \(884736\) | \(1.7913\) |
Rank
sage: E.rank()
The elliptic curves in class 117600.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 117600.bf do not have complex multiplication.Modular form 117600.2.a.bf
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.
