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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 304920.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304920.c1 | 304920c6 | \([0, 0, 0, -557857238763, -160373542652705338]\) | \(7259042500647479362626220802/12006225\) | \(31755581472987187200\) | \([2]\) | \(1132462080\) | \(4.8767\) | |
| 304920.c2 | 304920c4 | \([0, 0, 0, -34866077763, -2505836552585938]\) | \(3544454449806874081077604/144149438750625\) | \(190632328085257795820160000\) | \([2, 2]\) | \(566231040\) | \(4.5301\) | |
| 304920.c3 | 304920c5 | \([0, 0, 0, -34812716763, -2513888972946538]\) | \(-1764102724103262766456802/11303622506742021225\) | \(-29897249589503604650814754867200\) | \([2]\) | \(1132462080\) | \(4.8767\) | |
| 304920.c4 | 304920c3 | \([0, 0, 0, -3530102763, 14910826179062]\) | \(3678765970528905177604/2056287578994061875\) | \(2719364652363149468432979840000\) | \([2]\) | \(566231040\) | \(4.5301\) | |
| 304920.c5 | 304920c2 | \([0, 0, 0, -2182465263, -39027825703438]\) | \(3477299736386222510416/22070630703515625\) | \(7296899227959901536900000000\) | \([2, 2]\) | \(283115520\) | \(4.1835\) | |
| 304920.c6 | 304920c1 | \([0, 0, 0, -55512138, -1326730781563]\) | \(-915553975060166656/36269989013671875\) | \(-749464464754226074218750000\) | \([2]\) | \(141557760\) | \(3.8369\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304920.c have rank \(0\).
Complex multiplication
The elliptic curves in class 304920.c do not have complex multiplication.Modular form 304920.2.a.c
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.
