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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 23184bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23184.bl2 | 23184bp1 | \([0, 0, 0, -1179, 72522]\) | \(-60698457/725788\) | \(-2167191355392\) | \([2]\) | \(36864\) | \(1.0489\) | \(\Gamma_0(N)\)-optimal |
| 23184.bl1 | 23184bp2 | \([0, 0, 0, -34299, 2437290]\) | \(1494447319737/5411854\) | \(16159709454336\) | \([2]\) | \(73728\) | \(1.3955\) |
Rank
sage: E.rank()
The elliptic curves in class 23184bp have rank \(0\).
Complex multiplication
The elliptic curves in class 23184bp do not have complex multiplication.Modular form 23184.2.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.
