Properties

Label 7056.cd
Number of curves $2$
Conductor $7056$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.cd1 7056cb2 \([0, 0, 0, -16023, 778610]\) \(20720464/63\) \(1383235999488\) \([2]\) \(18432\) \(1.1983\)  
7056.cd2 7056cb1 \([0, 0, 0, -588, 22295]\) \(-16384/147\) \(-201721916592\) \([2]\) \(9216\) \(0.85170\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.cd have rank \(0\).

Complex multiplication

The elliptic curves in class 7056.cd do not have complex multiplication.

Modular form 7056.2.a.cd

sage: E.q_eigenform(10)
 
\(q + 4q^{5} + 2q^{11} + 6q^{13} - 4q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.