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Properties

Label 29302f
Number of curves $2$
Conductor $29302$
CM no
Rank $1$
Graph

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

Elliptic curves in class 29302f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29302.i2 29302f1 \([1, 1, 1, 272, 2449]\) \(45408227375/74381632\) \(-3644699968\) \([]\) \(18144\) \(0.51981\) \(\Gamma_0(N)\)-optimal
29302.i1 29302f2 \([1, 1, 1, -8828, 316945]\) \(-1552807715412625/7697866228\) \(-377195445172\) \([]\) \(54432\) \(1.0691\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29302f have rank \(1\).

Complex multiplication

The elliptic curves in class 29302f do not have complex multiplication.

Modular form 29302.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + 2 q^{6} + q^{8} + q^{9} + 3 q^{11} + 2 q^{12} - q^{13} + q^{16} + 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.