Properties

Label 2400.c
Number of curves $2$
Conductor $2400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2400.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.c1 2400y2 \([0, -1, 0, -48, -108]\) \(195112/9\) \(576000\) \([2]\) \(384\) \(-0.13318\)  
2400.c2 2400y1 \([0, -1, 0, 2, -8]\) \(64/3\) \(-24000\) \([2]\) \(192\) \(-0.47976\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2400.c have rank \(1\).

Complex multiplication

The elliptic curves in class 2400.c do not have complex multiplication.

Modular form 2400.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} - 6q^{11} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.