Properties

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

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

Elliptic curves in class 2400.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.t1 2400q1 \([0, 1, 0, -538, 4628]\) \(2156689088/81\) \(648000\) \([2]\) \(768\) \(0.20152\) \(\Gamma_0(N)\)-optimal
2400.t2 2400q2 \([0, 1, 0, -513, 5103]\) \(-29218112/6561\) \(-3359232000\) \([2]\) \(1536\) \(0.54809\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2400.2.a.t

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{7} + q^{9} + 4 q^{13} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.