Properties

Label 7056.bc
Number of curves $2$
Conductor $7056$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bc1 7056q2 \([0, 0, 0, -56595, -4605118]\) \(665500/81\) \(2440028303096832\) \([2]\) \(28672\) \(1.6830\)  
7056.bc2 7056q1 \([0, 0, 0, 5145, -369754]\) \(2000/9\) \(-67778563974912\) \([2]\) \(14336\) \(1.3364\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.bc have rank \(1\).

Complex multiplication

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

Modular form 7056.2.a.bc

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