Properties

Label 124950t
Number of curves $4$
Conductor $124950$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 124950t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.bb4 124950t1 \([1, 1, 0, 1200, -4320000]\) \(103823/4386816\) \(-8064133056000000\) \([2]\) \(1179648\) \(1.7311\) \(\Gamma_0(N)\)-optimal
124950.bb3 124950t2 \([1, 1, 0, -390800, -92520000]\) \(3590714269297/73410624\) \(134948226609000000\) \([2, 2]\) \(2359296\) \(2.0777\)  
124950.bb2 124950t3 \([1, 1, 0, -831800, 153999000]\) \(34623662831857/14438442312\) \(26541692180695125000\) \([2]\) \(4718592\) \(2.4242\)  
124950.bb1 124950t4 \([1, 1, 0, -6221800, -5975999000]\) \(14489843500598257/6246072\) \(11481939448875000\) \([2]\) \(4718592\) \(2.4242\)  

Rank

sage: E.rank()
 

The elliptic curves in class 124950t have rank \(1\).

Complex multiplication

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

Modular form 124950.2.a.t

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