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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 55506.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55506.a1 | 55506d3 | \([1, 1, 0, -8464682, -9482561760]\) | \(112763292123580561/1932612\) | \(1149562688044452\) | \([2]\) | \(2240000\) | \(2.4315\) | |
55506.a2 | 55506d4 | \([1, 1, 0, -8456272, -9502333670]\) | \(-112427521449300721/466873642818\) | \(-277707330708370558578\) | \([2]\) | \(4480000\) | \(2.7781\) | |
55506.a3 | 55506d1 | \([1, 1, 0, -37862, 2051220]\) | \(10091699281/2737152\) | \(1628121842721792\) | \([2]\) | \(448000\) | \(1.6268\) | \(\Gamma_0(N)\)-optimal |
55506.a4 | 55506d2 | \([1, 1, 0, 96698, 13488820]\) | \(168105213359/228637728\) | \(-135999052674854688\) | \([2]\) | \(896000\) | \(1.9734\) |
Rank
sage: E.rank()
The elliptic curves in class 55506.a have rank \(1\).
Complex multiplication
The elliptic curves in class 55506.a do not have complex multiplication.Modular form 55506.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.