Properties

Label 29232f
Number of curves $2$
Conductor $29232$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 29232f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29232.q2 29232f1 \([0, 0, 0, -19155, 1208482]\) \(-1041220466500/242597383\) \(-181097976019968\) \([2]\) \(73728\) \(1.4552\) \(\Gamma_0(N)\)-optimal
29232.q1 29232f2 \([0, 0, 0, -321915, 70298314]\) \(2471097448795250/98942809\) \(147720822294528\) \([2]\) \(147456\) \(1.8018\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29232f have rank \(1\).

Complex multiplication

The elliptic curves in class 29232f do not have complex multiplication.

Modular form 29232.2.a.f

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