Properties

Label 369600vj
Number of curves $2$
Conductor $369600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("vj1")
 
E.isogeny_class()
 

Elliptic curves in class 369600vj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.vj2 369600vj1 \([0, 1, 0, -525393, 145921743]\) \(7831544736466064/29831377653\) \(61094661433344000\) \([2]\) \(4571136\) \(2.0797\) \(\Gamma_0(N)\)-optimal
369600.vj1 369600vj2 \([0, 1, 0, -8398593, 9365438943]\) \(7997484869919944276/116700507\) \(956010553344000\) \([2]\) \(9142272\) \(2.4263\)  

Rank

sage: E.rank()
 

The elliptic curves in class 369600vj have rank \(1\).

Complex multiplication

The elliptic curves in class 369600vj do not have complex multiplication.

Modular form 369600.2.a.vj

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} - 4 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.