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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6018.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6018.h1 | 6018g1 | \([1, 1, 1, -52, -139]\) | \(15568817473/3081216\) | \(3081216\) | \([2]\) | \(960\) | \(-0.038524\) | \(\Gamma_0(N)\)-optimal |
6018.h2 | 6018g2 | \([1, 1, 1, 108, -651]\) | \(139233463487/289730592\) | \(-289730592\) | \([2]\) | \(1920\) | \(0.30805\) |
Rank
sage: E.rank()
The elliptic curves in class 6018.h have rank \(1\).
Complex multiplication
The elliptic curves in class 6018.h do not have complex multiplication.Modular form 6018.2.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.