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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 26450.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26450.q1 | 26450o4 | \([1, 1, 1, -1660013, 822543531]\) | \(-349938025/8\) | \(-11565303828125000\) | \([]\) | \(356400\) | \(2.1957\) | |
26450.q2 | 26450o3 | \([1, 1, 1, -6888, 2593531]\) | \(-25/2\) | \(-2891325957031250\) | \([]\) | \(118800\) | \(1.6464\) | |
26450.q3 | 26450o1 | \([1, 1, 1, -1598, -30309]\) | \(-121945/32\) | \(-118428711200\) | \([]\) | \(23760\) | \(0.84165\) | \(\Gamma_0(N)\)-optimal |
26450.q4 | 26450o2 | \([1, 1, 1, 11627, 223611]\) | \(46969655/32768\) | \(-121271000268800\) | \([]\) | \(71280\) | \(1.3910\) |
Rank
sage: E.rank()
The elliptic curves in class 26450.q have rank \(1\).
Complex multiplication
The elliptic curves in class 26450.q do not have complex multiplication.Modular form 26450.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.