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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 29575h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29575.k2 | 29575h1 | \([0, -1, 1, -5633, 182418]\) | \(-262144/35\) | \(-2639661171875\) | \([]\) | \(32832\) | \(1.1160\) | \(\Gamma_0(N)\)-optimal |
29575.k3 | 29575h2 | \([0, -1, 1, 36617, -472457]\) | \(71991296/42875\) | \(-3233584935546875\) | \([]\) | \(98496\) | \(1.6653\) | |
29575.k1 | 29575h3 | \([0, -1, 1, -554883, -166240332]\) | \(-250523582464/13671875\) | \(-1031117645263671875\) | \([]\) | \(295488\) | \(2.2147\) |
Rank
sage: E.rank()
The elliptic curves in class 29575h have rank \(0\).
Complex multiplication
The elliptic curves in class 29575h do not have complex multiplication.Modular form 29575.2.a.h
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.