Properties

Label 460c
Number of curves $2$
Conductor $460$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 460c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
460.c1 460c1 \([0, 1, 0, -46, 529]\) \(-687518464/7604375\) \(-121670000\) \([3]\) \(144\) \(0.23342\) \(\Gamma_0(N)\)-optimal
460.c2 460c2 \([0, 1, 0, 414, -13915]\) \(489277573376/5615234375\) \(-89843750000\) \([]\) \(432\) \(0.78273\)  

Rank

sage: E.rank()
 

The elliptic curves in class 460c have rank \(1\).

Complex multiplication

The elliptic curves in class 460c do not have complex multiplication.

Modular form 460.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 4 q^{7} - 2 q^{9} - 6 q^{11} - q^{13} - q^{15} + 2 q^{19} + O(q^{20})\) 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.