Properties

Label 382200.i
Number of curves $2$
Conductor $382200$
CM no
Rank $1$
Graph

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

Elliptic curves in class 382200.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.i1 382200i1 \([0, -1, 0, -543083, -153494088]\) \(14047232/39\) \(49180958531250000\) \([2]\) \(5017600\) \(2.0755\) \(\Gamma_0(N)\)-optimal
382200.i2 382200i2 \([0, -1, 0, -328708, -276116588]\) \(-194672/1521\) \(-30688918123500000000\) \([2]\) \(10035200\) \(2.4221\)  

Rank

sage: E.rank()
 

The elliptic curves in class 382200.i have rank \(1\).

Complex multiplication

The elliptic curves in class 382200.i do not have complex multiplication.

Modular form 382200.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 4 q^{11} - q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.