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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 21294.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21294.br1 | 21294cr2 | \([1, -1, 1, -94334, 11343557]\) | \(-156116857/2744\) | \(-1631768156751096\) | \([3]\) | \(168480\) | \(1.7163\) | |
21294.br2 | 21294cr1 | \([1, -1, 1, 4531, 72947]\) | \(17303/14\) | \(-8325347738526\) | \([]\) | \(56160\) | \(1.1670\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21294.br have rank \(0\).
Complex multiplication
The elliptic curves in class 21294.br do not have complex multiplication.Modular form 21294.2.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 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.