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SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 28560cv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.bo4 | 28560cv1 | \([0, -1, 0, -62480, -5990400]\) | \(6585576176607121/187425\) | \(767692800\) | \([2]\) | \(65536\) | \(1.2146\) | \(\Gamma_0(N)\)-optimal |
| 28560.bo3 | 28560cv2 | \([0, -1, 0, -62560, -5974208]\) | \(6610905152742241/35128130625\) | \(143884823040000\) | \([2, 2]\) | \(131072\) | \(1.5612\) | |
| 28560.bo5 | 28560cv3 | \([0, -1, 0, -28560, -12475008]\) | \(-629004249876241/16074715228425\) | \(-65842033575628800\) | \([2]\) | \(262144\) | \(1.9078\) | |
| 28560.bo2 | 28560cv4 | \([0, -1, 0, -97840, 1561600]\) | \(25288177725059761/14387797265625\) | \(58932417600000000\) | \([2, 4]\) | \(262144\) | \(1.9078\) | |
| 28560.bo6 | 28560cv5 | \([0, -1, 0, 387680, 12048832]\) | \(1573196002879828319/926055908203125\) | \(-3793125000000000000\) | \([4]\) | \(524288\) | \(2.2544\) | |
| 28560.bo1 | 28560cv6 | \([0, -1, 0, -1147840, 472801600]\) | \(40832710302042509761/91556816413125\) | \(375016720028160000\) | \([4]\) | \(524288\) | \(2.2544\) |
Rank
sage: E.rank()
The elliptic curves in class 28560cv have rank \(0\).
Complex multiplication
The elliptic curves in class 28560cv do not have complex multiplication.Modular form 28560.2.a.cv
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
