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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 50400.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50400.h1 | 50400bc4 | \([0, 0, 0, -42300, -3348000]\) | \(179406144/35\) | \(1632960000000\) | \([2]\) | \(147456\) | \(1.3432\) | |
50400.h2 | 50400bc3 | \([0, 0, 0, -18675, 951750]\) | \(123505992/4375\) | \(25515000000000\) | \([2]\) | \(147456\) | \(1.3432\) | |
50400.h3 | 50400bc1 | \([0, 0, 0, -2925, -40500]\) | \(3796416/1225\) | \(893025000000\) | \([2, 2]\) | \(73728\) | \(0.99662\) | \(\Gamma_0(N)\)-optimal |
50400.h4 | 50400bc2 | \([0, 0, 0, 8325, -276750]\) | \(10941048/12005\) | \(-70013160000000\) | \([2]\) | \(147456\) | \(1.3432\) |
Rank
sage: E.rank()
The elliptic curves in class 50400.h have rank \(2\).
Complex multiplication
The elliptic curves in class 50400.h do not have complex multiplication.Modular form 50400.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.