# Properties

 Label 7350s Number of curves $2$ Conductor $7350$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 7350s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.r2 7350s1 $$[1, 1, 0, 1200, 1800]$$ $$2595575/1512$$ $$-111178305000$$ $$[]$$ $$10368$$ $$0.80897$$ $$\Gamma_0(N)$$-optimal
7350.r1 7350s2 $$[1, 1, 0, -17175, 909525]$$ $$-7620530425/526848$$ $$-38739462720000$$ $$[]$$ $$31104$$ $$1.3583$$

## Rank

sage: E.rank()

The elliptic curves in class 7350s have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7350s do not have complex multiplication.

## Modular form7350.2.a.s

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 6q^{11} - q^{12} + q^{13} + q^{16} - 3q^{17} - q^{18} + 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 