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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 212940br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212940.bb4 | 212940br1 | \([0, 0, 0, -58812, 5485909]\) | \(10788913152/8575\) | \(17880431259600\) | \([2]\) | \(622080\) | \(1.4732\) | \(\Gamma_0(N)\)-optimal |
| 212940.bb3 | 212940br2 | \([0, 0, 0, -71487, 2948374]\) | \(1210991472/588245\) | \(19625561350536960\) | \([2]\) | \(1244160\) | \(1.8198\) | |
| 212940.bb2 | 212940br3 | \([0, 0, 0, -200772, -28532439]\) | \(588791808/109375\) | \(166260642707250000\) | \([2]\) | \(1866240\) | \(2.0225\) | |
| 212940.bb1 | 212940br4 | \([0, 0, 0, -3052647, -2052793314]\) | \(129348709488/6125\) | \(148969535865696000\) | \([2]\) | \(3732480\) | \(2.3691\) |
Rank
sage: E.rank()
The elliptic curves in class 212940br have rank \(1\).
Complex multiplication
The elliptic curves in class 212940br do not have complex multiplication.Modular form 212940.2.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.
