Properties

Label 6350400.y
Number of curves $2$
Conductor $6350400$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("y1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 6350400.y have rank \(0\).

Complex multiplication

The elliptic curves in class 6350400.y do not have complex multiplication.

Modular form 6350400.2.a.y

Copy content sage:E.q_eigenform(10)
 
\(q - 6 q^{11} - 2 q^{13} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 6350400.y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
6350400.y1 \([0, 0, 0, -17066700, 43841574000]\) \(-2146689/2000\) \(-512192530096128000000000\) \([]\) \(752467968\) \(3.2459\)
6350400.y2 \([0, 0, 0, 1749300, -1028314000]\) \(15166431/20480\) \(-799398187499520000000\) \([]\) \(250822656\) \(2.6966\)