Properties

Label 234234db
Number of curves $2$
Conductor $234234$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 234234db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234234.db2 234234db1 \([1, -1, 1, -616037, -290505315]\) \(-7347774183121/6119866368\) \(-21534241600553730048\) \([2]\) \(10321920\) \(2.4075\) \(\Gamma_0(N)\)-optimal
234234.db1 234234db2 \([1, -1, 1, -11323877, -14660426595]\) \(45637459887836881/13417633152\) \(47213212940986764672\) \([2]\) \(20643840\) \(2.7541\)  

Rank

sage: E.rank()
 

The elliptic curves in class 234234db have rank \(1\).

Complex multiplication

The elliptic curves in class 234234db do not have complex multiplication.

Modular form 234234.2.a.db

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{5} - q^{7} + q^{8} - 4 q^{10} - q^{11} - q^{14} + q^{16} + 4 q^{17} + 2 q^{19} + O(q^{20})\) 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.