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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 45760.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45760.br1 | 45760o4 | \([0, -1, 0, -1497985, -705179775]\) | \(1418098748958579169/8307406250\) | \(2177736704000000\) | \([2]\) | \(884736\) | \(2.1327\) | |
| 45760.br2 | 45760o3 | \([0, -1, 0, -91905, -11419903]\) | \(-327495950129089/26547449500\) | \(-6959254601728000\) | \([2]\) | \(442368\) | \(1.7861\) | |
| 45760.br3 | 45760o2 | \([0, -1, 0, -26625, -26623]\) | \(7962857630209/4606058600\) | \(1207450625638400\) | \([2]\) | \(294912\) | \(1.5834\) | |
| 45760.br4 | 45760o1 | \([0, -1, 0, 6655, -6655]\) | \(124326214271/71980480\) | \(-18869250949120\) | \([2]\) | \(147456\) | \(1.2368\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45760.br have rank \(0\).
Complex multiplication
The elliptic curves in class 45760.br do not have complex multiplication.Modular form 45760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
