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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 92400.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92400.cw1 | 92400be6 | \([0, -1, 0, -12806640008, 557833047898512]\) | \(7259042500647479362626220802/12006225\) | \(384199200000000\) | \([2]\) | \(56623104\) | \(3.9331\) | |
| 92400.cw2 | 92400be4 | \([0, -1, 0, -800415008, 8716341298512]\) | \(3544454449806874081077604/144149438750625\) | \(2306391020010000000000\) | \([2, 2]\) | \(28311552\) | \(3.5865\) | |
| 92400.cw3 | 92400be5 | \([0, -1, 0, -799190008, 8744349698512]\) | \(-1764102724103262766456802/11303622506742021225\) | \(-361715920215744679200000000\) | \([2]\) | \(56623104\) | \(3.9331\) | |
| 92400.cw4 | 92400be3 | \([0, -1, 0, -81040008, -51837451488]\) | \(3678765970528905177604/2056287578994061875\) | \(32900601263904990000000000\) | \([2]\) | \(28311552\) | \(3.5865\) | |
| 92400.cw5 | 92400be2 | \([0, -1, 0, -50102508, 135767548512]\) | \(3477299736386222510416/22070630703515625\) | \(88282522814062500000000\) | \([2, 2]\) | \(14155776\) | \(3.2400\) | |
| 92400.cw6 | 92400be1 | \([0, -1, 0, -1274383, 4615204762]\) | \(-915553975060166656/36269989013671875\) | \(-9067497253417968750000\) | \([2]\) | \(7077888\) | \(2.8934\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.cw have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.cw do not have complex multiplication.Modular form 92400.2.a.cw
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
