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SageMath
E = EllipticCurve("sb1")
E.isogeny_class()
Elliptic curves in class 369600.sb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.sb1 | 369600sb4 | \([0, 1, 0, -33124033, 20778272063]\) | \(981281029968144361/522287841796875\) | \(2139291000000000000000000\) | \([2]\) | \(56623104\) | \(3.3599\) | |
| 369600.sb2 | 369600sb2 | \([0, 1, 0, -25996033, 50951096063]\) | \(474334834335054841/607815140625\) | \(2489610816000000000000\) | \([2, 2]\) | \(28311552\) | \(3.0133\) | |
| 369600.sb3 | 369600sb1 | \([0, 1, 0, -25988033, 50984064063]\) | \(473897054735271721/779625\) | \(3193344000000000\) | \([2]\) | \(14155776\) | \(2.6668\) | \(\Gamma_0(N)\)-optimal |
| 369600.sb4 | 369600sb3 | \([0, 1, 0, -18996033, 79014096063]\) | \(-185077034913624841/551466161890875\) | \(-2258805399105024000000000\) | \([2]\) | \(56623104\) | \(3.3599\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.sb have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.sb do not have complex multiplication.Modular form 369600.2.a.sb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
