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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 46255.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46255.e1 | 46255i4 | \([1, -1, 1, -49777, 4285854]\) | \(22930509321/6875\) | \(4089410331875\) | \([2]\) | \(96768\) | \(1.3980\) | |
| 46255.e2 | 46255i3 | \([1, -1, 1, -24547, -1439674]\) | \(2749884201/73205\) | \(43544041213805\) | \([2]\) | \(96768\) | \(1.3980\) | |
| 46255.e3 | 46255i2 | \([1, -1, 1, -3522, 48896]\) | \(8120601/3025\) | \(1799340546025\) | \([2, 2]\) | \(48384\) | \(1.0514\) | |
| 46255.e4 | 46255i1 | \([1, -1, 1, 683, 5164]\) | \(59319/55\) | \(-32715282655\) | \([2]\) | \(24192\) | \(0.70483\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46255.e have rank \(1\).
Complex multiplication
The elliptic curves in class 46255.e do not have complex multiplication.Modular form 46255.2.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.
