Properties

Label 31200.s
Number of curves $2$
Conductor $31200$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 31200.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.s1 31200bo1 \([0, -1, 0, -264758, 52428012]\) \(2052450196928704/4317958125\) \(4317958125000000\) \([2]\) \(221184\) \(1.8852\) \(\Gamma_0(N)\)-optimal
31200.s2 31200bo2 \([0, -1, 0, -173633, 88969137]\) \(-9045718037056/48125390625\) \(-3080025000000000000\) \([2]\) \(442368\) \(2.2318\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31200.s have rank \(1\).

Complex multiplication

The elliptic curves in class 31200.s do not have complex multiplication.

Modular form 31200.2.a.s

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} - 2 q^{11} + q^{13} + 2 q^{17} - 2 q^{19} + O(q^{20})\)  Toggle raw display

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.