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Properties

Label 462d
Number of curves $2$
Conductor $462$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 462d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462.d2 462d1 \([1, 0, 1, -1676, 5058506]\) \(-520203426765625/11054534935707648\) \(-11054534935707648\) \([2]\) \(4160\) \(1.7574\) \(\Gamma_0(N)\)-optimal
462.d1 462d2 \([1, 0, 1, -452236, 115355594]\) \(10228636028672744397625/167006381634183168\) \(167006381634183168\) \([2]\) \(8320\) \(2.1039\)  

Rank

sage: E.rank()
 

The elliptic curves in class 462d have rank \(0\).

Complex multiplication

The elliptic curves in class 462d do not have complex multiplication.

Modular form 462.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + q^{12} + 6 q^{13} + q^{14} + q^{16} + 4 q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.