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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 8256.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8256.bl1 | 8256bp2 | \([0, 1, 0, -3833665, 2888210111]\) | \(-23769846831649063249/3261823333284\) | \(-855067415880400896\) | \([]\) | \(225792\) | \(2.4586\) | |
| 8256.bl2 | 8256bp1 | \([0, 1, 0, 10175, -879169]\) | \(444369620591/1540767744\) | \(-403903019483136\) | \([]\) | \(32256\) | \(1.4857\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8256.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 8256.bl do not have complex multiplication.Modular form 8256.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
