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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 35574h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35574.g2 | 35574h1 | \([1, 1, 0, -970, 52144]\) | \(-9625/108\) | \(-1134387198252\) | \([]\) | \(47520\) | \(0.99508\) | \(\Gamma_0(N)\)-optimal |
35574.g1 | 35574h2 | \([1, 1, 0, -140725, 20260717]\) | \(-29343015625/192\) | \(-2016688352448\) | \([]\) | \(142560\) | \(1.5444\) |
Rank
sage: E.rank()
The elliptic curves in class 35574h have rank \(1\).
Complex multiplication
The elliptic curves in class 35574h do not have complex multiplication.Modular form 35574.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.