Properties

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

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Show commands: SageMath
E = EllipticCurve("bpr1")
 
E.isogeny_class()
 

Elliptic curves in class 6350400.bpr

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
6350400.bpr1 \([0, 0, 0, -17654700, 28675486000]\) \(-15590912409/78125\) \(-3049462080000000000000\) \([]\) \(340623360\) \(2.9698\)
6350400.bpr2 \([0, 0, 0, -14700, -21266000]\) \(-9/5\) \(-195165573120000000\) \([]\) \(48660480\) \(1.9968\)

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6350400.2.a.bpr

sage: E.q_eigenform(10)
 
\(q + 2 q^{11} + 2 q^{13} + 4 q^{17} - 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.