Properties

Label 3528.b
Number of curves $2$
Conductor $3528$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3528.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3528.b1 3528ba2 \([0, 0, 0, -17787, -902090]\) \(3543122/49\) \(8606801774592\) \([2]\) \(9216\) \(1.2876\)  
3528.b2 3528ba1 \([0, 0, 0, -147, -37730]\) \(-4/7\) \(-614771555328\) \([2]\) \(4608\) \(0.94102\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3528.b have rank \(0\).

Complex multiplication

The elliptic curves in class 3528.b do not have complex multiplication.

Modular form 3528.2.a.b

sage: E.q_eigenform(10)
 
\(q - 4q^{5} - 2q^{17} + 2q^{19} + O(q^{20})\)  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.