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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 37026z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.bg1 | 37026z1 | \([1, -1, 1, -215645, 38596385]\) | \(858729462625/38148\) | \(49266920081412\) | \([2]\) | \(245760\) | \(1.7047\) | \(\Gamma_0(N)\)-optimal |
37026.bg2 | 37026z2 | \([1, -1, 1, -204755, 42660533]\) | \(-735091890625/181908738\) | \(-234929308408213122\) | \([2]\) | \(491520\) | \(2.0513\) |
Rank
sage: E.rank()
The elliptic curves in class 37026z have rank \(0\).
Complex multiplication
The elliptic curves in class 37026z do not have complex multiplication.Modular form 37026.2.a.z
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.