Show commands:
SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 15246bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.ba2 | 15246bp1 | \([1, -1, 1, -44672, -3285345]\) | \(5735339/588\) | \(1010738993642532\) | \([2]\) | \(135168\) | \(1.6147\) | \(\Gamma_0(N)\)-optimal |
15246.ba1 | 15246bp2 | \([1, -1, 1, -164462, 22110135]\) | \(286191179/43218\) | \(74289316032726102\) | \([2]\) | \(270336\) | \(1.9613\) |
Rank
sage: E.rank()
The elliptic curves in class 15246bp have rank \(0\).
Complex multiplication
The elliptic curves in class 15246bp do not have complex multiplication.Modular form 15246.2.a.bp
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 Cremona 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 Cremona labels.