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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 52325.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52325.h1 | 52325c1 | \([0, -1, 1, -1092183, 439694643]\) | \(-9221261135586623488/121324931\) | \(-1895702046875\) | \([]\) | \(373248\) | \(1.9143\) | \(\Gamma_0(N)\)-optimal |
52325.h2 | 52325c2 | \([0, -1, 1, -1030433, 491540268]\) | \(-7743965038771437568/2189290237869371\) | \(-34207659966708921875\) | \([]\) | \(1119744\) | \(2.4636\) |
Rank
sage: E.rank()
The elliptic curves in class 52325.h have rank \(0\).
Complex multiplication
The elliptic curves in class 52325.h do not have complex multiplication.Modular form 52325.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.