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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 51520.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51520.bg1 | 51520w4 | \([0, 0, 0, -13772, 622064]\) | \(4407931365156/100625\) | \(6594560000\) | \([2]\) | \(40960\) | \(0.99764\) | |
| 51520.bg2 | 51520w3 | \([0, 0, 0, -3692, -77264]\) | \(84923690436/9794435\) | \(641888092160\) | \([2]\) | \(40960\) | \(0.99764\) | |
| 51520.bg3 | 51520w2 | \([0, 0, 0, -892, 8976]\) | \(4790692944/648025\) | \(10617241600\) | \([2, 2]\) | \(20480\) | \(0.65107\) | |
| 51520.bg4 | 51520w1 | \([0, 0, 0, 88, 744]\) | \(73598976/276115\) | \(-282741760\) | \([2]\) | \(10240\) | \(0.30450\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 51520.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 51520.bg do not have complex multiplication.Modular form 51520.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
