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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 374790h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374790.h4 | 374790h1 | \([1, 1, 0, -1261882873, -21099185282267]\) | \(-250386371942892200094169/71782716130983936000\) | \(-63707424798426321351868416000\) | \([2]\) | \(454164480\) | \(4.2421\) | \(\Gamma_0(N)\)-optimal |
374790.h3 | 374790h2 | \([1, 1, 0, -21415513593, -1206209255415003]\) | \(1223880546761358893859301849/69832897265664000000\) | \(61976953378171634909184000000\) | \([2, 2]\) | \(908328960\) | \(4.5886\) | |
374790.h2 | 374790h3 | \([1, 1, 0, -22645593593, -1059875740407003]\) | \(1447120434734326449115621849/290670009882258329856000\) | \(257970703726810644340112199936000\) | \([2]\) | \(1816657920\) | \(4.9352\) | |
374790.h1 | 374790h4 | \([1, 1, 0, -342643525113, -77199184186303707]\) | \(5012808770744123733046717639129/16321500000000000\) | \(14485391329441500000000000\) | \([2]\) | \(1816657920\) | \(4.9352\) |
Rank
sage: E.rank()
The elliptic curves in class 374790h have rank \(1\).
Complex multiplication
The elliptic curves in class 374790h do not have complex multiplication.Modular form 374790.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.