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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 28050.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.h1 | 28050o1 | \([1, 1, 0, -4950, 132000]\) | \(858729462625/38148\) | \(596062500\) | \([2]\) | \(36864\) | \(0.76114\) | \(\Gamma_0(N)\)-optimal |
28050.h2 | 28050o2 | \([1, 1, 0, -4700, 146250]\) | \(-735091890625/181908738\) | \(-2842324031250\) | \([2]\) | \(73728\) | \(1.1077\) |
Rank
sage: E.rank()
The elliptic curves in class 28050.h have rank \(1\).
Complex multiplication
The elliptic curves in class 28050.h do not have complex multiplication.Modular form 28050.2.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.