Properties

Label 350658.di
Number of curves $2$
Conductor $350658$
CM no
Rank $0$
Graph

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

Elliptic curves in class 350658.di

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.di1 350658di2 \([1, -1, 1, -144414590, -667945834531]\) \(3776104682692733708238625/3408048\) \(300620506032\) \([]\) \(19906560\) \(2.8825\)  
350658.di2 350658di1 \([1, -1, 1, -1783310, -915406819]\) \(7110352307247726625/6866458324992\) \(605683422389219328\) \([]\) \(6635520\) \(2.3332\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 350658.di have rank \(0\).

Complex multiplication

The elliptic curves in class 350658.di do not have complex multiplication.

Modular form 350658.2.a.di

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.