Properties

Label 29400.ba
Number of curves $2$
Conductor $29400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29400.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.ba1 29400co1 \([0, -1, 0, -1283, 13812]\) \(2725888/675\) \(57881250000\) \([2]\) \(18432\) \(0.77547\) \(\Gamma_0(N)\)-optimal
29400.ba2 29400co2 \([0, -1, 0, 3092, 83812]\) \(2382032/3645\) \(-5000940000000\) \([2]\) \(36864\) \(1.1220\)  

Rank

sage: E.rank()
 

The elliptic curves in class 29400.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 29400.ba do not have complex multiplication.

Modular form 29400.2.a.ba

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