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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 346560.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 346560.e1 | 346560e4 | \([0, -1, 0, -693601, -222106079]\) | \(23937672968/45\) | \(69371974287360\) | \([2]\) | \(3686400\) | \(1.9111\) | |
| 346560.e2 | 346560e3 | \([0, -1, 0, -116001, 10724481]\) | \(111980168/32805\) | \(50572169255485440\) | \([2]\) | \(3686400\) | \(1.9111\) | |
| 346560.e3 | 346560e2 | \([0, -1, 0, -43801, -3383399]\) | \(48228544/2025\) | \(390217355366400\) | \([2, 2]\) | \(1843200\) | \(1.5645\) | |
| 346560.e4 | 346560e1 | \([0, -1, 0, 1324, -197574]\) | \(85184/5625\) | \(-16936517160000\) | \([2]\) | \(921600\) | \(1.2180\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346560.e have rank \(1\).
Complex multiplication
The elliptic curves in class 346560.e do not have complex multiplication.Modular form 346560.2.a.e
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.
