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Properties

Label 474075di
Number of curves $2$
Conductor $474075$
CM no
Rank $2$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("di1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 474075di have rank \(2\).

Complex multiplication

The elliptic curves in class 474075di do not have complex multiplication.

Modular form 474075.2.a.di

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{8} + 2 q^{11} + 2 q^{13} - q^{16} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 474075di

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
474075.di1 474075di1 \([1, -1, 0, -248292, 46727491]\) \(1263214441/29025\) \(38896275969140625\) \([2]\) \(3981312\) \(1.9696\) \(\Gamma_0(N)\)-optimal
474075.di2 474075di2 \([1, -1, 0, 27333, 144574366]\) \(1685159/6739605\) \(-9031715280034453125\) \([2]\) \(7962624\) \(2.3162\)