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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 26450.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26450.i1 | 26450i2 | \([1, 0, 1, -66401, 6580348]\) | \(-349938025/8\) | \(-740179445000\) | \([]\) | \(71280\) | \(1.3910\) | |
26450.i2 | 26450i3 | \([1, 0, 1, -39951, -3708702]\) | \(-121945/32\) | \(-1850448612500000\) | \([]\) | \(118800\) | \(1.6464\) | |
26450.i3 | 26450i1 | \([1, 0, 1, -276, 20748]\) | \(-25/2\) | \(-185044861250\) | \([]\) | \(23760\) | \(0.84165\) | \(\Gamma_0(N)\)-optimal |
26450.i4 | 26450i4 | \([1, 0, 1, 290674, 27370048]\) | \(46969655/32768\) | \(-1894859379200000000\) | \([]\) | \(356400\) | \(2.1957\) |
Rank
sage: E.rank()
The elliptic curves in class 26450.i have rank \(1\).
Complex multiplication
The elliptic curves in class 26450.i do not have complex multiplication.Modular form 26450.2.a.i
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.
\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.