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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 26026.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26026.q1 | 26026l2 | \([1, 0, 0, -413, -5071]\) | \(-46105515625/38162432\) | \(-6449451008\) | \([]\) | \(13824\) | \(0.58020\) | |
26026.q2 | 26026l1 | \([1, 0, 0, 42, 116]\) | \(48410375/60368\) | \(-10202192\) | \([]\) | \(4608\) | \(0.030899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26026.q have rank \(1\).
Complex multiplication
The elliptic curves in class 26026.q do not have complex multiplication.Modular form 26026.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.