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Properties

Label 434112di
Number of curves $2$
Conductor $434112$
CM no
Rank $0$
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 434112di have rank \(0\).

Complex multiplication

The elliptic curves in class 434112di do not have complex multiplication.

Modular form 434112.2.a.di

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} - q^{17} + q^{19} + O(q^{20})\) 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 434112di

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
434112.di1 434112di1 \([0, 1, 0, -14372673, 19915984575]\) \(1252553990449987212625/70889922816427008\) \(18583367926789441585152\) \([2]\) \(24084480\) \(3.0276\) \(\Gamma_0(N)\)-optimal
434112.di2 434112di2 \([0, 1, 0, 10213567, 81032459967]\) \(449485901393767859375/11080072238736418848\) \(-2904574456951319782490112\) \([2]\) \(48168960\) \(3.3742\)