# Properties

 Label 3025.a Number of curves $3$ Conductor $3025$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 3025.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3025.a1 3025g3 $$[0, 1, 1, -23656508, 44278891894]$$ $$-52893159101157376/11$$ $$-304487046875$$ $$[]$$ $$84000$$ $$2.5004$$
3025.a2 3025g2 $$[0, 1, 1, -31258, 3842394]$$ $$-122023936/161051$$ $$-4457994853296875$$ $$[]$$ $$16800$$ $$1.6957$$
3025.a3 3025g1 $$[0, 1, 1, -1008, -29606]$$ $$-4096/11$$ $$-304487046875$$ $$[]$$ $$3360$$ $$0.89094$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3025.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3025.a do not have complex multiplication.

## Modular form3025.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{2} + q^{3} + 2q^{4} - 2q^{6} - 2q^{7} - 2q^{9} + 2q^{12} + 4q^{13} + 4q^{14} - 4q^{16} - 2q^{17} + 4q^{18} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 