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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 13680br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13680.bk3 | 13680br1 | \([0, 0, 0, -4467, 114226]\) | \(3301293169/22800\) | \(68080435200\) | \([2]\) | \(12288\) | \(0.91222\) | \(\Gamma_0(N)\)-optimal |
| 13680.bk2 | 13680br2 | \([0, 0, 0, -7347, -51086]\) | \(14688124849/8122500\) | \(24253655040000\) | \([2, 2]\) | \(24576\) | \(1.2588\) | |
| 13680.bk1 | 13680br3 | \([0, 0, 0, -89427, -10278254]\) | \(26487576322129/44531250\) | \(132969600000000\) | \([2]\) | \(49152\) | \(1.6054\) | |
| 13680.bk4 | 13680br4 | \([0, 0, 0, 28653, -403886]\) | \(871257511151/527800050\) | \(-1576002504499200\) | \([2]\) | \(49152\) | \(1.6054\) |
Rank
sage: E.rank()
The elliptic curves in class 13680br have rank \(1\).
Complex multiplication
The elliptic curves in class 13680br do not have complex multiplication.Modular form 13680.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
