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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 22218.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22218.h1 | 22218i2 | \([1, 1, 0, -535094, -150441540]\) | \(9407293631/31752\) | \(57190199306773176\) | \([2]\) | \(317952\) | \(2.0795\) | |
22218.h2 | 22218i1 | \([1, 1, 0, -48414, -57420]\) | \(6967871/4032\) | \(7262247531018816\) | \([2]\) | \(158976\) | \(1.7329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22218.h have rank \(1\).
Complex multiplication
The elliptic curves in class 22218.h do not have complex multiplication.Modular form 22218.2.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.