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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 21294.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21294.bu1 | 21294cm4 | \([1, -1, 1, -2044256, -1124484825]\) | \(268498407453697/252\) | \(886723427772\) | \([2]\) | \(245760\) | \(2.0209\) | |
| 21294.bu2 | 21294cm6 | \([1, -1, 1, -1390226, 625212735]\) | \(84448510979617/933897762\) | \(3286146923449362882\) | \([2]\) | \(491520\) | \(2.3675\) | |
| 21294.bu3 | 21294cm3 | \([1, -1, 1, -158216, -8533209]\) | \(124475734657/63011844\) | \(221722532944105284\) | \([2, 2]\) | \(245760\) | \(2.0209\) | |
| 21294.bu4 | 21294cm2 | \([1, -1, 1, -127796, -17537529]\) | \(65597103937/63504\) | \(223454303798544\) | \([2, 2]\) | \(122880\) | \(1.6743\) | |
| 21294.bu5 | 21294cm1 | \([1, -1, 1, -6116, -404985]\) | \(-7189057/16128\) | \(-56750299377408\) | \([2]\) | \(61440\) | \(1.3277\) | \(\Gamma_0(N)\)-optimal |
| 21294.bu6 | 21294cm5 | \([1, -1, 1, 587074, -66367713]\) | \(6359387729183/4218578658\) | \(-14844097333125252738\) | \([2]\) | \(491520\) | \(2.3675\) |
Rank
sage: E.rank()
The elliptic curves in class 21294.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 21294.bu do not have complex multiplication.Modular form 21294.2.a.bu
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
