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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 13520.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13520.n1 | 13520n3 | \([0, 0, 0, -3749603, 2794641122]\) | \(294889639316481/260\) | \(5140358512640\) | \([2]\) | \(129024\) | \(2.1714\) | |
| 13520.n2 | 13520n2 | \([0, 0, 0, -234403, 43645602]\) | \(72043225281/67600\) | \(1336493213286400\) | \([2, 2]\) | \(64512\) | \(1.8248\) | |
| 13520.n3 | 13520n4 | \([0, 0, 0, -180323, 64314978]\) | \(-32798729601/71402500\) | \(-1411670956533760000\) | \([2]\) | \(129024\) | \(2.1714\) | |
| 13520.n4 | 13520n1 | \([0, 0, 0, -18083, 338338]\) | \(33076161/16640\) | \(328982944808960\) | \([2]\) | \(32256\) | \(1.4783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13520.n have rank \(0\).
Complex multiplication
The elliptic curves in class 13520.n do not have complex multiplication.Modular form 13520.2.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.
