# Properties

 Label 7605.d Number of curves $2$ Conductor $7605$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 7605.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7605.d1 7605n2 $$[1, -1, 1, -2625278, -1636478944]$$ $$258840217117/18225$$ $$140891643782162325$$ $$$$ $$119808$$ $$2.3433$$
7605.d2 7605n1 $$[1, -1, 1, -153653, -28934044]$$ $$-51895117/16875$$ $$-130455225724224375$$ $$$$ $$59904$$ $$1.9967$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7605.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - q^{5} + 2 q^{7} + 3 q^{8} + q^{10} - 2 q^{14} - q^{16} + 2 q^{17} + 2 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 