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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 301665.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301665.br1 | 301665br4 | \([1, 1, 0, -10342972, -12807439991]\) | \(25351269426118370449/27551475\) | \(132985707493275\) | \([2]\) | \(7077888\) | \(2.4289\) | |
| 301665.br2 | 301665br3 | \([1, 1, 0, -806302, -93945509]\) | \(12010404962647729/6166198828125\) | \(29763063999383203125\) | \([2]\) | \(7077888\) | \(2.4289\) | |
| 301665.br3 | 301665br2 | \([1, 1, 0, -646597, -200213216]\) | \(6193921595708449/6452105625\) | \(31143081499700625\) | \([2, 2]\) | \(3538944\) | \(2.0823\) | |
| 301665.br4 | 301665br1 | \([1, 1, 0, -30592, -4693229]\) | \(-656008386769/1581036975\) | \(-7631363500262775\) | \([2]\) | \(1769472\) | \(1.7357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301665.br have rank \(0\).
Complex multiplication
The elliptic curves in class 301665.br do not have complex multiplication.Modular form 301665.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
