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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 161700.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
161700.br1 | 161700dj2 | \([0, -1, 0, -93508, -10884488]\) | \(192143824/1815\) | \(854131740000000\) | \([2]\) | \(884736\) | \(1.6858\) | |
161700.br2 | 161700dj1 | \([0, -1, 0, -1633, -410738]\) | \(-16384/2475\) | \(-72795318750000\) | \([2]\) | \(442368\) | \(1.3393\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 161700.br have rank \(0\).
Complex multiplication
The elliptic curves in class 161700.br do not have complex multiplication.Modular form 161700.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.