Properties

Label 50400ci
Number of curves $2$
Conductor $50400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ci1")
 
E.isogeny_class()
 

Elliptic curves in class 50400ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50400.i2 50400ci1 \([0, 0, 0, -112425, 1079500]\) \(5820343774272/3349609375\) \(90439453125000000\) \([2]\) \(368640\) \(1.9432\) \(\Gamma_0(N)\)-optimal
50400.i1 50400ci2 \([0, 0, 0, -1284300, 558892000]\) \(135574940230848/367653125\) \(635304600000000000\) \([2]\) \(737280\) \(2.2898\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50400ci have rank \(0\).

Complex multiplication

The elliptic curves in class 50400ci do not have complex multiplication.

Modular form 50400.2.a.ci

sage: E.q_eigenform(10)
 
\(q - q^{7} - 4 q^{11} + 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.