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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 279312.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 279312.bp1 | 279312bp3 | \([0, -1, 0, -372592, 87662608]\) | \(37736227588/33\) | \(5002428761088\) | \([2]\) | \(2433024\) | \(1.7371\) | |
| 279312.bp2 | 279312bp4 | \([0, -1, 0, -55192, -3063008]\) | \(122657188/43923\) | \(6658232681008128\) | \([2]\) | \(2433024\) | \(1.7371\) | |
| 279312.bp3 | 279312bp2 | \([0, -1, 0, -23452, 1355200]\) | \(37642192/1089\) | \(41270037278976\) | \([2, 2]\) | \(1216512\) | \(1.3905\) | |
| 279312.bp4 | 279312bp1 | \([0, -1, 0, 353, 69730]\) | \(2048/891\) | \(-2110399633584\) | \([2]\) | \(608256\) | \(1.0439\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 279312.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 279312.bp do not have complex multiplication.Modular form 279312.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
