Properties

Label 355740.dn
Number of curves $2$
Conductor $355740$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dn1")
 
E.isogeny_class()
 

Elliptic curves in class 355740.dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.dn1 355740dn1 \([0, 1, 0, -3351861, 2360798460]\) \(1248870793216/42525\) \(141810587412555600\) \([2]\) \(8064000\) \(2.3828\) \(\Gamma_0(N)\)-optimal
355740.dn2 355740dn2 \([0, 1, 0, -3203636, 2579222820]\) \(-68150496976/14467005\) \(-771903389404022641920\) \([2]\) \(16128000\) \(2.7294\)  

Rank

sage: E.rank()
 

The elliptic curves in class 355740.dn have rank \(1\).

Complex multiplication

The elliptic curves in class 355740.dn do not have complex multiplication.

Modular form 355740.2.a.dn

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + q^{9} + 4 q^{13} - q^{15} + 2 q^{17} + 2 q^{19} + O(q^{20})\) 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 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.