Properties

Label 378560dq
Number of curves $2$
Conductor $378560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dq1")
 
E.isogeny_class()
 

Elliptic curves in class 378560dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
378560.dq1 378560dq1 \([0, 0, 0, -9141548, -10638366128]\) \(267080942160036/1990625\) \(629693917798400000\) \([2]\) \(12042240\) \(2.5913\) \(\Gamma_0(N)\)-optimal
378560.dq2 378560dq2 \([0, 0, 0, -8952268, -11099982192]\) \(-125415986034978/11552734375\) \(-7308947260160000000000\) \([2]\) \(24084480\) \(2.9379\)  

Rank

sage: E.rank()
 

The elliptic curves in class 378560dq have rank \(0\).

Complex multiplication

The elliptic curves in class 378560dq do not have complex multiplication.

Modular form 378560.2.a.dq

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 3 q^{9} - 2 q^{11} - 8 q^{19} + O(q^{20})\) 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.