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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 24640.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24640.b1 | 24640bc4 | \([0, 1, 0, -225281, 40856575]\) | \(4823468134087681/30382271150\) | \(7964530088345600\) | \([2]\) | \(221184\) | \(1.8885\) | |
| 24640.b2 | 24640bc2 | \([0, 1, 0, -17281, -842625]\) | \(2177286259681/105875000\) | \(27754496000000\) | \([2]\) | \(73728\) | \(1.3392\) | |
| 24640.b3 | 24640bc3 | \([0, 1, 0, -5761, 1386879]\) | \(-80677568161/3131816380\) | \(-820986873118720\) | \([2]\) | \(110592\) | \(1.5420\) | |
| 24640.b4 | 24640bc1 | \([0, 1, 0, 639, -50561]\) | \(109902239/4312000\) | \(-1130364928000\) | \([2]\) | \(36864\) | \(0.99266\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24640.b have rank \(0\).
Complex multiplication
The elliptic curves in class 24640.b do not have complex multiplication.Modular form 24640.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
