Properties

Label 46800.i
Number of curves $2$
Conductor $46800$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 46800.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.i1 46800bt2 \([0, 0, 0, -2115, 36450]\) \(5606442/169\) \(31539456000\) \([2]\) \(40960\) \(0.79096\)  
46800.i2 46800bt1 \([0, 0, 0, -315, -1350]\) \(37044/13\) \(1213056000\) \([2]\) \(20480\) \(0.44439\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.i have rank \(2\).

Complex multiplication

The elliptic curves in class 46800.i do not have complex multiplication.

Modular form 46800.2.a.i

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 2q^{11} + q^{13} - 4q^{17} + 2q^{19} + O(q^{20})\)  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.