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Properties

Label 124950.c
Number of curves $2$
Conductor $124950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 124950.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.c1 124950cb2 \([1, 1, 0, -1406325, 3797302125]\) \(-6693187811305/131714173248\) \(-6053140925177325000000\) \([]\) \(9331200\) \(2.8605\)  
124950.c2 124950cb1 \([1, 1, 0, 155550, -137061000]\) \(9056932295/181997172\) \(-8363978628370312500\) \([]\) \(3110400\) \(2.3112\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 124950.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 6 q^{11} - q^{12} + 4 q^{13} + q^{16} - q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.