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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 361998.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361998.h1 | 361998h1 | \([1, -1, 0, -17014698, 25188433024]\) | \(154813496529595177/11724454211652\) | \(41255350108380648503172\) | \([2]\) | \(34062336\) | \(3.0846\) | \(\Gamma_0(N)\)-optimal |
361998.h2 | 361998h2 | \([1, -1, 0, 16401672, 111997479010]\) | \(138675717957047543/1620336115431306\) | \(-5701547596896883811581866\) | \([2]\) | \(68124672\) | \(3.4312\) |
Rank
sage: E.rank()
The elliptic curves in class 361998.h have rank \(1\).
Complex multiplication
The elliptic curves in class 361998.h do not have complex multiplication.Modular form 361998.2.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.