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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 13680.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13680.n1 | 13680g4 | \([0, 0, 0, -273603, 55084498]\) | \(3034301922374404/1425\) | \(1063756800\) | \([4]\) | \(32768\) | \(1.5058\) | |
| 13680.n2 | 13680g3 | \([0, 0, 0, -20523, 491722]\) | \(1280615525284/601171875\) | \(448772400000000\) | \([2]\) | \(32768\) | \(1.5058\) | |
| 13680.n3 | 13680g2 | \([0, 0, 0, -17103, 860398]\) | \(2964647793616/2030625\) | \(378963360000\) | \([2, 2]\) | \(16384\) | \(1.1592\) | |
| 13680.n4 | 13680g1 | \([0, 0, 0, -858, 18907]\) | \(-5988775936/9774075\) | \(-114004810800\) | \([2]\) | \(8192\) | \(0.81261\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13680.n have rank \(0\).
Complex multiplication
The elliptic curves in class 13680.n do not have complex multiplication.Modular form 13680.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
