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Properties

Label 57330.m
Number of curves $2$
Conductor $57330$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 57330.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57330.m1 57330g2 \([1, -1, 0, -23506485, -43860131659]\) \(620307836233921107/2548000000\) \(5900366060316000000\) \([2]\) \(3538944\) \(2.8117\)  
57330.m2 57330g1 \([1, -1, 0, -1491765, -662848075]\) \(158542456758867/9691136000\) \(22441620855693312000\) \([2]\) \(1769472\) \(2.4652\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 57330.m have rank \(1\).

Complex multiplication

The elliptic curves in class 57330.m do not have complex multiplication.

Modular form 57330.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2 q^{11} + q^{13} + q^{16} + 4 q^{17} + 4 q^{19} + O(q^{20})\) 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.