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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 73920.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.b1 | 73920eh6 | \([0, -1, 0, -2049062401, 35701724877985]\) | \(7259042500647479362626220802/12006225\) | \(1573679923200\) | \([4]\) | \(18874368\) | \(3.4750\) | |
| 73920.b2 | 73920eh4 | \([0, -1, 0, -128066401, 557871456385]\) | \(3544454449806874081077604/144149438750625\) | \(9446977617960960000\) | \([2, 2]\) | \(9437184\) | \(3.1284\) | |
| 73920.b3 | 73920eh5 | \([0, -1, 0, -127870401, 559663954785]\) | \(-1764102724103262766456802/11303622506742021225\) | \(-1481588409203690206003200\) | \([2]\) | \(18874368\) | \(3.4750\) | |
| 73920.b4 | 73920eh3 | \([0, -1, 0, -12966401, -3315003615]\) | \(3678765970528905177604/2056287578994061875\) | \(134760862776954839040000\) | \([2]\) | \(9437184\) | \(3.1284\) | |
| 73920.b5 | 73920eh2 | \([0, -1, 0, -8016401, 8690726385]\) | \(3477299736386222510416/22070630703515625\) | \(361605213446400000000\) | \([2, 2]\) | \(4718592\) | \(2.7818\) | |
| 73920.b6 | 73920eh1 | \([0, -1, 0, -203901, 295413885]\) | \(-915553975060166656/36269989013671875\) | \(-37140468750000000000\) | \([2]\) | \(2359296\) | \(2.4353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.b have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.b do not have complex multiplication.Modular form 73920.2.a.b
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.
