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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 24990.cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24990.cb1 | 24990bx8 | \([1, 0, 0, -5560031, 5045705895]\) | \(161572377633716256481/914742821250\) | \(107618578177241250\) | \([2]\) | \(786432\) | \(2.4597\) | |
| 24990.cb2 | 24990bx4 | \([1, 0, 0, -1066241, -423859815]\) | \(1139466686381936641/4080\) | \(480007920\) | \([2]\) | \(196608\) | \(1.7665\) | |
| 24990.cb3 | 24990bx6 | \([1, 0, 0, -353781, 75819645]\) | \(41623544884956481/2962701562500\) | \(348558876126562500\) | \([2, 2]\) | \(393216\) | \(2.1131\) | |
| 24990.cb4 | 24990bx3 | \([1, 0, 0, -70561, -5804359]\) | \(330240275458561/67652010000\) | \(7959191324490000\) | \([2, 2]\) | \(196608\) | \(1.7665\) | |
| 24990.cb5 | 24990bx2 | \([1, 0, 0, -66641, -6626775]\) | \(278202094583041/16646400\) | \(1958432313600\) | \([2, 2]\) | \(98304\) | \(1.4200\) | |
| 24990.cb6 | 24990bx1 | \([1, 0, 0, -3921, -116439]\) | \(-56667352321/16711680\) | \(-1966112440320\) | \([2]\) | \(49152\) | \(1.0734\) | \(\Gamma_0(N)\)-optimal |
| 24990.cb7 | 24990bx5 | \([1, 0, 0, 149939, -34778059]\) | \(3168685387909439/6278181696900\) | \(-738621798458588100\) | \([2]\) | \(393216\) | \(2.1131\) | |
| 24990.cb8 | 24990bx7 | \([1, 0, 0, 320949, 331002531]\) | \(31077313442863199/420227050781250\) | \(-49439292297363281250\) | \([2]\) | \(786432\) | \(2.4597\) |
Rank
sage: E.rank()
The elliptic curves in class 24990.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 24990.cb do not have complex multiplication.Modular form 24990.2.a.cb
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
