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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 159120.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159120.b1 | 159120bd3 | \([0, 0, 0, -11033283, 14082028738]\) | \(49745123032831462081/97939634471640\) | \(292446181498165493760\) | \([2]\) | \(8847360\) | \(2.8151\) | |
| 159120.b2 | 159120bd4 | \([0, 0, 0, -9247683, -10768074302]\) | \(29291056630578924481/175463302795560\) | \(523930614734697431040\) | \([2]\) | \(8847360\) | \(2.8151\) | |
| 159120.b3 | 159120bd2 | \([0, 0, 0, -924483, 57079618]\) | \(29263955267177281/16463793153600\) | \(49160622935959142400\) | \([2, 2]\) | \(4423680\) | \(2.4686\) | |
| 159120.b4 | 159120bd1 | \([0, 0, 0, 227517, 7082818]\) | \(436192097814719/259683840000\) | \(-775411791298560000\) | \([2]\) | \(2211840\) | \(2.1220\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159120.b have rank \(1\).
Complex multiplication
The elliptic curves in class 159120.b do not have complex multiplication.Modular form 159120.2.a.b
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.
