Properties

Label 37485.i
Number of curves $2$
Conductor $37485$
CM no
Rank $1$
Graph

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

Elliptic curves in class 37485.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37485.i1 37485f2 \([1, -1, 1, -13313, 594542]\) \(82142689923/425\) \(1350022275\) \([2]\) \(36864\) \(0.94867\)  
37485.i2 37485f1 \([1, -1, 1, -818, 9776]\) \(-19034163/1445\) \(-4590075735\) \([2]\) \(18432\) \(0.60210\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37485.i have rank \(1\).

Complex multiplication

The elliptic curves in class 37485.i do not have complex multiplication.

Modular form 37485.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} + 3 q^{8} + q^{10} - 2 q^{11} - 2 q^{13} - q^{16} + q^{17} + O(q^{20})\) 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.