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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 63210br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63210.bs1 | 63210br1 | \([1, 1, 1, -9360, -325263]\) | \(770842973809/66873600\) | \(7867612166400\) | \([2]\) | \(184320\) | \(1.2152\) | \(\Gamma_0(N)\)-optimal |
63210.bs2 | 63210br2 | \([1, 1, 1, 10240, -1485583]\) | \(1009328859791/8734528080\) | \(-1027608494083920\) | \([2]\) | \(368640\) | \(1.5618\) |
Rank
sage: E.rank()
The elliptic curves in class 63210br have rank \(0\).
Complex multiplication
The elliptic curves in class 63210br do not have complex multiplication.Modular form 63210.2.a.br
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.