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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 44880.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44880.s1 | 44880bi4 | \([0, -1, 0, -2854816, 1616922880]\) | \(628200507126935410849/88124751829125000\) | \(360958983492096000000\) | \([2]\) | \(1990656\) | \(2.6708\) | |
44880.s2 | 44880bi2 | \([0, -1, 0, -729376, -239239424]\) | \(10476561483361670689/13992628953600\) | \(57313808193945600\) | \([2]\) | \(663552\) | \(2.1215\) | |
44880.s3 | 44880bi1 | \([0, -1, 0, -33056, -5832960]\) | \(-975276594443809/3037581803520\) | \(-12441935067217920\) | \([2]\) | \(331776\) | \(1.7749\) | \(\Gamma_0(N)\)-optimal |
44880.s4 | 44880bi3 | \([0, -1, 0, 289504, 135319296]\) | \(655127711084516831/2313151512408000\) | \(-9474668594823168000\) | \([2]\) | \(995328\) | \(2.3242\) |
Rank
sage: E.rank()
The elliptic curves in class 44880.s have rank \(1\).
Complex multiplication
The elliptic curves in class 44880.s do not have complex multiplication.Modular form 44880.2.a.s
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.