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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 70560br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.ec3 | 70560br1 | \([0, 0, 0, -2315397, 1355792564]\) | \(250094631024064/62015625\) | \(340405734249000000\) | \([2, 2]\) | \(1179648\) | \(2.3517\) | \(\Gamma_0(N)\)-optimal |
| 70560.ec4 | 70560br2 | \([0, 0, 0, -2039772, 1690732064]\) | \(-2671731885376/1969120125\) | \(-691748023927951872000\) | \([2]\) | \(2359296\) | \(2.6982\) | |
| 70560.ec2 | 70560br3 | \([0, 0, 0, -2593227, 1010005346]\) | \(43919722445768/15380859375\) | \(675408202875000000000\) | \([2]\) | \(2359296\) | \(2.6982\) | |
| 70560.ec1 | 70560br4 | \([0, 0, 0, -37044147, 86781571814]\) | \(128025588102048008/7875\) | \(345808999872000\) | \([2]\) | \(2359296\) | \(2.6982\) |
Rank
sage: E.rank()
The elliptic curves in class 70560br have rank \(0\).
Complex multiplication
The elliptic curves in class 70560br do not have complex multiplication.Modular form 70560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
