Properties

Label 7350.bh
Number of curves $2$
Conductor $7350$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.bh1 7350z1 \([1, 0, 1, -376, -1102]\) \(1092727/540\) \(2894062500\) \([2]\) \(4608\) \(0.50859\) \(\Gamma_0(N)\)-optimal
7350.bh2 7350z2 \([1, 0, 1, 1374, -8102]\) \(53582633/36450\) \(-195349218750\) \([2]\) \(9216\) \(0.85516\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7350.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 7350.bh do not have complex multiplication.

Modular form 7350.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 2q^{11} + q^{12} - 2q^{13} + q^{16} + 4q^{17} - q^{18} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.