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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 15210.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.bf1 | 15210bl1 | \([1, -1, 1, -34163213, 74032843317]\) | \(570403428460237/23887872000\) | \(184669495338155802624000\) | \([2]\) | \(2695680\) | \(3.2292\) | \(\Gamma_0(N)\)-optimal |
| 15210.bf2 | 15210bl2 | \([1, -1, 1, 16455667, 274625340981]\) | \(63745936931123/4251528000000\) | \(-32867202661502827176000000\) | \([2]\) | \(5391360\) | \(3.5758\) |
Rank
sage: E.rank()
The elliptic curves in class 15210.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 15210.bf do not have complex multiplication.Modular form 15210.2.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.
