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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 24990.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.h1 | 24990b2 | \([1, 1, 0, -568523, 164758077]\) | \(172735174415217961/39657600\) | \(4665676982400\) | \([2]\) | \(241920\) | \(1.8116\) | |
24990.h2 | 24990b1 | \([1, 1, 0, -35403, 2582973]\) | \(-41713327443241/639221760\) | \(-75203800842240\) | \([2]\) | \(120960\) | \(1.4651\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24990.h have rank \(0\).
Complex multiplication
The elliptic curves in class 24990.h do not have complex multiplication.Modular form 24990.2.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.