# Properties

 Label 7605.j Number of curves $2$ Conductor $7605$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 7605.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7605.j1 7605a1 $$[0, 0, 1, -7098, 231234]$$ $$-303464448/1625$$ $$-211776244875$$ $$[]$$ $$8064$$ $$1.0178$$ $$\Gamma_0(N)$$-optimal
7605.j2 7605a2 $$[0, 0, 1, 18252, 1230869]$$ $$7077888/10985$$ $$-1043641805793795$$ $$[]$$ $$24192$$ $$1.5671$$

## Rank

sage: E.rank()

The elliptic curves in class 7605.j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7605.j do not have complex multiplication.

## Modular form7605.2.a.j

sage: E.q_eigenform(10)

$$q - 2 q^{4} - q^{5} + q^{7} + 3 q^{11} + 4 q^{16} - 3 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.