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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 82810.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.h1 | 82810bl2 | \([1, 0, 1, -201283, 34740318]\) | \(544737993463/20000\) | \(33111909740000\) | \([2]\) | \(737280\) | \(1.6819\) | |
82810.h2 | 82810bl1 | \([1, 0, 1, -12003, 594206]\) | \(-115501303/25600\) | \(-42383244467200\) | \([2]\) | \(368640\) | \(1.3353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 82810.h have rank \(1\).
Complex multiplication
The elliptic curves in class 82810.h do not have complex multiplication.Modular form 82810.2.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 LMFDB 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 LMFDB labels.