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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 12480cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12480.cy3 | 12480cu1 | \([0, 1, 0, -6406460, 6239168358]\) | \(454357982636417669333824/3003024375\) | \(192193560000\) | \([2]\) | \(215040\) | \(2.2241\) | \(\Gamma_0(N)\)-optimal |
| 12480.cy2 | 12480cu2 | \([0, 1, 0, -6406585, 6238912583]\) | \(7099759044484031233216/577161945398025\) | \(2364055328350310400\) | \([2, 2]\) | \(430080\) | \(2.5707\) | |
| 12480.cy1 | 12480cu3 | \([0, 1, 0, -6845985, 5333660703]\) | \(1082883335268084577352/251301565117746585\) | \(8234649685778320097280\) | \([2]\) | \(860160\) | \(2.9173\) | |
| 12480.cy4 | 12480cu4 | \([0, 1, 0, -5969185, 7127796863]\) | \(-717825640026599866952/254764560814329735\) | \(-8348125128763956756480\) | \([2]\) | \(860160\) | \(2.9173\) |
Rank
sage: E.rank()
The elliptic curves in class 12480cu have rank \(0\).
Complex multiplication
The elliptic curves in class 12480cu do not have complex multiplication.Modular form 12480.2.a.cu
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.
