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Properties

Label 303450.da
Number of curves $2$
Conductor $303450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("da1")
 
E.isogeny_class()
 

Elliptic curves in class 303450.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.da1 303450da1 \([1, 0, 1, -19744631, 33769858778]\) \(-287137850384705/22020096\) \(-65282910622502092800\) \([]\) \(19584000\) \(2.8503\) \(\Gamma_0(N)\)-optimal
303450.da2 303450da2 \([1, 0, 1, 104849049, 66446418298]\) \(110072002975/65345616\) \(-75675760154574093281250000\) \([]\) \(97920000\) \(3.6550\)  

Rank

sage: E.rank()
 

The elliptic curves in class 303450.da have rank \(1\).

Complex multiplication

The elliptic curves in class 303450.da do not have complex multiplication.

Modular form 303450.2.a.da

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + q^{12} + 4 q^{13} - q^{14} + q^{16} - q^{18} - 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.