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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 141610br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141610.c2 | 141610br1 | \([1, 0, 1, -36160409, -83696507268]\) | \(1841373668746009/31443200\) | \(89291168524771539200\) | \([2]\) | \(16588800\) | \(2.9577\) | \(\Gamma_0(N)\)-optimal |
| 141610.c3 | 141610br2 | \([1, 0, 1, -35027529, -89185537444]\) | \(-1673672305534489/241375690000\) | \(-685449235878441518890000\) | \([2]\) | \(33177600\) | \(3.3043\) | |
| 141610.c1 | 141610br3 | \([1, 0, 1, -59030424, 34332510566]\) | \(8010684753304969/4456448000000\) | \(12655246583995301888000000\) | \([2]\) | \(49766400\) | \(3.5070\) | |
| 141610.c4 | 141610br4 | \([1, 0, 1, 230986856, 271914666342]\) | \(479958568556831351/289000000000000\) | \(-820690887176209000000000000\) | \([2]\) | \(99532800\) | \(3.8536\) |
Rank
sage: E.rank()
The elliptic curves in class 141610br have rank \(0\).
Complex multiplication
The elliptic curves in class 141610br do not have complex multiplication.Modular form 141610.2.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 Cremona 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 Cremona labels.
