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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 43120.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43120.h1 | 43120bx2 | \([0, 1, 0, -43136, 3379060]\) | \(18420660721/336875\) | \(162336796160000\) | \([2]\) | \(196608\) | \(1.5216\) | |
43120.h2 | 43120bx1 | \([0, 1, 0, -16, 153684]\) | \(-1/21175\) | \(-10204027187200\) | \([2]\) | \(98304\) | \(1.1750\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43120.h have rank \(2\).
Complex multiplication
The elliptic curves in class 43120.h do not have complex multiplication.Modular form 43120.2.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.