Properties

Label 129600cb
Number of curves $2$
Conductor $129600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 129600cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129600.is1 129600cb1 \([0, 0, 0, -9900, 414000]\) \(-35937/4\) \(-11943936000000\) \([]\) \(248832\) \(1.2466\) \(\Gamma_0(N)\)-optimal
129600.is2 129600cb2 \([0, 0, 0, 62100, -594000]\) \(109503/64\) \(-15479341056000000\) \([]\) \(746496\) \(1.7959\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129600cb have rank \(1\).

Complex multiplication

The elliptic curves in class 129600cb do not have complex multiplication.

Modular form 129600.2.a.cb

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.