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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 141120.ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.ej1 | 141120hi3 | \([0, 0, 0, -1317708, -510169968]\) | \(416832723/56000\) | \(33994407923417088000\) | \([2]\) | \(2654208\) | \(2.4752\) | |
| 141120.ej2 | 141120hi1 | \([0, 0, 0, -329868, 72831248]\) | \(4767078987/6860\) | \(5712366214840320\) | \([2]\) | \(884736\) | \(1.9259\) | \(\Gamma_0(N)\)-optimal |
| 141120.ej3 | 141120hi2 | \([0, 0, 0, -235788, 115242512]\) | \(-1740992427/5882450\) | \(-4898354029225574400\) | \([2]\) | \(1769472\) | \(2.2725\) | |
| 141120.ej4 | 141120hi4 | \([0, 0, 0, 2069172, -2700803952]\) | \(1613964717/6125000\) | \(-3718138366623744000000\) | \([2]\) | \(5308416\) | \(2.8218\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.ej have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.ej do not have complex multiplication.Modular form 141120.2.a.ej
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
