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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 119952.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.bh1 | 119952gt6 | \([0, 0, 0, -195761811, 1054241418706]\) | \(2361739090258884097/5202\) | \(1827452360466432\) | \([2]\) | \(9437184\) | \(3.0625\) | |
| 119952.bh2 | 119952gt4 | \([0, 0, 0, -12235251, 16472132530]\) | \(576615941610337/27060804\) | \(9506407179146379264\) | \([2, 2]\) | \(4718592\) | \(2.7159\) | |
| 119952.bh3 | 119952gt5 | \([0, 0, 0, -11600211, 18258246034]\) | \(-491411892194497/125563633938\) | \(-44110257444971374583808\) | \([2]\) | \(9437184\) | \(3.0625\) | |
| 119952.bh4 | 119952gt2 | \([0, 0, 0, -804531, 229079410]\) | \(163936758817/30338064\) | \(10657702166240231424\) | \([2, 2]\) | \(2359296\) | \(2.3693\) | |
| 119952.bh5 | 119952gt1 | \([0, 0, 0, -240051, -41983886]\) | \(4354703137/352512\) | \(123836771721019392\) | \([2]\) | \(1179648\) | \(2.0228\) | \(\Gamma_0(N)\)-optimal |
| 119952.bh6 | 119952gt3 | \([0, 0, 0, 1594509, 1334077234]\) | \(1276229915423/2927177028\) | \(-1028311528127972917248\) | \([2]\) | \(4718592\) | \(2.7159\) |
Rank
sage: E.rank()
The elliptic curves in class 119952.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.bh do not have complex multiplication.Modular form 119952.2.a.bh
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
