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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 52878h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52878.f1 | 52878h1 | \([1, 0, 0, -5459, 136545]\) | \(17991524611989937/2303563655232\) | \(2303563655232\) | \([2]\) | \(158400\) | \(1.1010\) | \(\Gamma_0(N)\)-optimal |
52878.f2 | 52878h2 | \([1, 0, 0, 8261, 715529]\) | \(62347392184415183/256831397226936\) | \(-256831397226936\) | \([2]\) | \(316800\) | \(1.4476\) |
Rank
sage: E.rank()
The elliptic curves in class 52878h have rank \(1\).
Complex multiplication
The elliptic curves in class 52878h do not have complex multiplication.Modular form 52878.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.