Properties

Label 29624.o
Number of curves $2$
Conductor $29624$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 29624.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29624.o1 29624j2 \([0, -1, 0, -258328, -50446596]\) \(12576878500/1127\) \(170840521628672\) \([2]\) \(168960\) \(1.7710\)  
29624.o2 29624j1 \([0, -1, 0, -14988, -902572]\) \(-9826000/3703\) \(-140333285623552\) \([2]\) \(84480\) \(1.4244\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29624.o have rank \(1\).

Complex multiplication

The elliptic curves in class 29624.o do not have complex multiplication.

Modular form 29624.2.a.o

sage: E.q_eigenform(10)
 
\(q + 2q^{3} + q^{7} + q^{9} - 4q^{11} + 6q^{13} + O(q^{20})\)  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.