Properties

Label 62400.i
Number of curves $2$
Conductor $62400$
CM no
Rank $2$
Graph

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

Elliptic curves in class 62400.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
62400.i1 62400fy2 \([0, -1, 0, -993, 4257]\) \(26463592/13689\) \(56070144000\) \([2]\) \(57344\) \(0.75452\)  
62400.i2 62400fy1 \([0, -1, 0, -793, 8857]\) \(107850176/117\) \(59904000\) \([2]\) \(28672\) \(0.40795\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62400.i have rank \(2\).

Complex multiplication

The elliptic curves in class 62400.i do not have complex multiplication.

Modular form 62400.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} - 2q^{11} + q^{13} + 2q^{19} + O(q^{20})\)  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.