Properties

Label 705600.caw
Number of curves $2$
Conductor $705600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("caw1")
 
E.isogeny_class()
 

Elliptic curves in class 705600.caw

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.caw1 \([0, 0, 0, -4050864300, 99236092686640]\) \(266916252066900625/162\) \(4461766039948492800\) \([]\) \(278691840\) \(3.8012\)
705600.caw2 \([0, 0, 0, -50112300, 135545285680]\) \(505318200625/4251528\) \(117094587952408245043200\) \([]\) \(92897280\) \(3.2519\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.caw have rank \(0\).

Complex multiplication

The elliptic curves in class 705600.caw do not have complex multiplication.

Modular form 705600.2.a.caw

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