Properties

 Label 37296ba Number of curves $2$ Conductor $37296$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

Elliptic curves in class 37296ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37296.cc2 37296ba1 $$[0, 0, 0, 141, -28478]$$ $$415292/469567$$ $$-350529887232$$ $$$$ $$41472$$ $$0.89422$$ $$\Gamma_0(N)$$-optimal
37296.cc1 37296ba2 $$[0, 0, 0, -13179, -569270]$$ $$169556172914/4353013$$ $$6499013584896$$ $$$$ $$82944$$ $$1.2408$$

Rank

sage: E.rank()

The elliptic curves in class 37296ba have rank $$1$$.

Complex multiplication

The elliptic curves in class 37296ba do not have complex multiplication.

Modular form 37296.2.a.ba

sage: E.q_eigenform(10)

$$q + 2 q^{5} + q^{7} + 4 q^{11} - 6 q^{13} + 4 q^{17} - 4 q^{19} + O(q^{20})$$ 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 Cremona 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 Cremona labels. 