Show commands:
SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 113256.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
113256.br1 | 113256o4 | \([0, 0, 0, -331419, -71637082]\) | \(3044193988/85293\) | \(112796853739435008\) | \([2]\) | \(1474560\) | \(2.0511\) | |
113256.br2 | 113256o2 | \([0, 0, 0, -48279, 2488970]\) | \(37642192/13689\) | \(4525799687076096\) | \([2, 2]\) | \(737280\) | \(1.7045\) | |
113256.br3 | 113256o1 | \([0, 0, 0, -42834, 3411353]\) | \(420616192/117\) | \(2417628037968\) | \([2]\) | \(368640\) | \(1.3579\) | \(\Gamma_0(N)\)-optimal |
113256.br4 | 113256o3 | \([0, 0, 0, 147741, 17582510]\) | \(269676572/257049\) | \(-339937843162604544\) | \([2]\) | \(1474560\) | \(2.0511\) |
Rank
sage: E.rank()
The elliptic curves in class 113256.br have rank \(1\).
Complex multiplication
The elliptic curves in class 113256.br do not have complex multiplication.Modular form 113256.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.