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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 260100.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 260100.bl1 | 260100bl1 | \([0, 0, 0, -392700, -94730375]\) | \(-127157223424/16875\) | \(-888810468750000\) | \([]\) | \(1492992\) | \(1.8880\) | \(\Gamma_0(N)\)-optimal |
| 260100.bl2 | 260100bl2 | \([0, 0, 0, 66300, -298755875]\) | \(611926016/732421875\) | \(-38576843261718750000\) | \([]\) | \(4478976\) | \(2.4373\) |
Rank
sage: E.rank()
The elliptic curves in class 260100.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 260100.bl do not have complex multiplication.Modular form 260100.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
