# Properties

 Label 7056.h Number of curves $2$ Conductor $7056$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.h1 7056bj2 $$[0, 0, 0, -13419, -598374]$$ $$-67645179/8$$ $$-31603654656$$ $$[]$$ $$10368$$ $$1.0402$$
7056.h2 7056bj1 $$[0, 0, 0, 21, -2534]$$ $$189/512$$ $$-2774532096$$ $$[]$$ $$3456$$ $$0.49093$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7056.h have rank $$1$$.

## Complex multiplication

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

## Modular form7056.2.a.h

sage: E.q_eigenform(10)

$$q - 3q^{5} + 3q^{11} - 2q^{13} - 6q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 