Properties

Label 124950.ii
Number of curves $4$
Conductor $124950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ii1")
 
E.isogeny_class()
 

Elliptic curves in class 124950.ii

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.ii1 124950hi3 \([1, 0, 0, -919388, 256453392]\) \(46753267515625/11591221248\) \(21307743571968000000\) \([2]\) \(3732480\) \(2.4191\)  
124950.ii2 124950hi1 \([1, 0, 0, -313013, -67405983]\) \(1845026709625/793152\) \(1458024057000000\) \([2]\) \(1244160\) \(1.8698\) \(\Gamma_0(N)\)-optimal
124950.ii3 124950hi2 \([1, 0, 0, -264013, -89210983]\) \(-1107111813625/1228691592\) \(-2258661517300125000\) \([2]\) \(2488320\) \(2.2164\)  
124950.ii4 124950hi4 \([1, 0, 0, 2216612, 1626885392]\) \(655215969476375/1001033261568\) \(-1840165034222088000000\) \([2]\) \(7464960\) \(2.7657\)  

Rank

sage: E.rank()
 

The elliptic curves in class 124950.ii have rank \(0\).

Complex multiplication

The elliptic curves in class 124950.ii do not have complex multiplication.

Modular form 124950.2.a.ii

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + 2 q^{13} + q^{16} - q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.