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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 141120.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.bm1 | 141120ll6 | \([0, 0, 0, -5645388, -5162841488]\) | \(1770025017602/75\) | \(843115275878400\) | \([2]\) | \(3145728\) | \(2.3488\) | |
| 141120.bm2 | 141120ll4 | \([0, 0, 0, -353388, -80404688]\) | \(868327204/5625\) | \(31616822845440000\) | \([2, 2]\) | \(1572864\) | \(2.0023\) | |
| 141120.bm3 | 141120ll5 | \([0, 0, 0, -141708, -175830032]\) | \(-27995042/1171875\) | \(-13173676185600000000\) | \([2]\) | \(3145728\) | \(2.3488\) | |
| 141120.bm4 | 141120ll2 | \([0, 0, 0, -35868, 499408]\) | \(3631696/2025\) | \(2845514056089600\) | \([2, 2]\) | \(786432\) | \(1.6557\) | |
| 141120.bm5 | 141120ll1 | \([0, 0, 0, -27048, 1709512]\) | \(24918016/45\) | \(3952102855680\) | \([2]\) | \(393216\) | \(1.3091\) | \(\Gamma_0(N)\)-optimal |
| 141120.bm6 | 141120ll3 | \([0, 0, 0, 140532, 3956848]\) | \(54607676/32805\) | \(-184389310834606080\) | \([2]\) | \(1572864\) | \(2.0023\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.bm do not have complex multiplication.Modular form 141120.2.a.bm
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.
