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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 166410.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.h1 | 166410ct2 | \([1, -1, 0, -3248115, -1552921219]\) | \(30459021867/9245000\) | \(1150294230320102415000\) | \([2]\) | \(8515584\) | \(2.7462\) | |
166410.h2 | 166410ct1 | \([1, -1, 0, -1251195, 520281125]\) | \(1740992427/68800\) | \(8560329155870529600\) | \([2]\) | \(4257792\) | \(2.3996\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.h have rank \(2\).
Complex multiplication
The elliptic curves in class 166410.h do not have complex multiplication.Modular form 166410.2.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.