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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 26520.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26520.b1 | 26520o1 | \([0, -1, 0, -356, -2460]\) | \(19545784144/89505\) | \(22913280\) | \([2]\) | \(7168\) | \(0.26314\) | \(\Gamma_0(N)\)-optimal |
26520.b2 | 26520o2 | \([0, -1, 0, -176, -5124]\) | \(-592143556/10989225\) | \(-11252966400\) | \([2]\) | \(14336\) | \(0.60971\) |
Rank
sage: E.rank()
The elliptic curves in class 26520.b have rank \(1\).
Complex multiplication
The elliptic curves in class 26520.b do not have complex multiplication.Modular form 26520.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.