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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 90480cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90480.cb3 | 90480cc1 | \([0, 1, 0, -28360, -1847692]\) | \(615882348586441/21715200\) | \(88945459200\) | \([2]\) | \(294912\) | \(1.1907\) | \(\Gamma_0(N)\)-optimal |
| 90480.cb2 | 90480cc2 | \([0, 1, 0, -29640, -1673100]\) | \(703093388853961/115124490000\) | \(471549911040000\) | \([2, 2]\) | \(589824\) | \(1.5373\) | |
| 90480.cb4 | 90480cc3 | \([0, 1, 0, 53880, -9323532]\) | \(4223169036960119/11647532812500\) | \(-47708294400000000\) | \([2]\) | \(1179648\) | \(1.8839\) | |
| 90480.cb1 | 90480cc4 | \([0, 1, 0, -133640, 17171700]\) | \(64443098670429961/6032611833300\) | \(24709578069196800\) | \([4]\) | \(1179648\) | \(1.8839\) |
Rank
sage: E.rank()
The elliptic curves in class 90480cc have rank \(0\).
Complex multiplication
The elliptic curves in class 90480cc do not have complex multiplication.Modular form 90480.2.a.cc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
