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Properties

Label 1470e
Number of curves $2$
Conductor $1470$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 1470e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.e1 1470e1 \([1, 1, 0, -32, -174]\) \(-77626969/182250\) \(-8930250\) \([]\) \(432\) \(0.022038\) \(\Gamma_0(N)\)-optimal
1470.e2 1470e2 \([1, 1, 0, 283, 3669]\) \(50872947671/140625000\) \(-6890625000\) \([]\) \(1296\) \(0.57134\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1470e have rank \(1\).

Complex multiplication

The elliptic curves in class 1470e do not have complex multiplication.

Modular form 1470.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 3 q^{11} - q^{12} - 5 q^{13} - q^{15} + q^{16} - q^{18} - 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.