Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 46200.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.n1 | 46200c4 | \([0, -1, 0, -211408, 37382812]\) | \(65308549273636/204604785\) | \(3273676560000000\) | \([2]\) | \(294912\) | \(1.8444\) | |
| 46200.n2 | 46200c2 | \([0, -1, 0, -18908, 37812]\) | \(186906097744/108056025\) | \(432224100000000\) | \([2, 2]\) | \(147456\) | \(1.4978\) | |
| 46200.n3 | 46200c1 | \([0, -1, 0, -12783, -550188]\) | \(924093773824/3565485\) | \(891371250000\) | \([2]\) | \(73728\) | \(1.1512\) | \(\Gamma_0(N)\)-optimal |
| 46200.n4 | 46200c3 | \([0, -1, 0, 75592, 226812]\) | \(2985557859644/1729468125\) | \(-27671490000000000\) | \([2]\) | \(294912\) | \(1.8444\) |
Rank
sage: E.rank()
The elliptic curves in class 46200.n have rank \(0\).
Complex multiplication
The elliptic curves in class 46200.n do not have complex multiplication.Modular form 46200.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
