Properties

Label 3520m
Number of curves $2$
Conductor $3520$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 3520m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3520.k1 3520m1 \([0, -1, 0, -65, 577]\) \(-117649/440\) \(-115343360\) \([]\) \(768\) \(0.23262\) \(\Gamma_0(N)\)-optimal
3520.k2 3520m2 \([0, -1, 0, 575, -13375]\) \(80062991/332750\) \(-87228416000\) \([]\) \(2304\) \(0.78192\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3520m have rank \(1\).

Complex multiplication

The elliptic curves in class 3520m do not have complex multiplication.

Modular form 3520.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} - 2 q^{9} + q^{11} - 2 q^{13} - q^{15} - 3 q^{17} + q^{19} + O(q^{20})\) 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.