Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 179776.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179776.y1 | 179776bf2 | \([0, 1, 0, -424994209, 3372434610367]\) | \(-9814089221/1024\) | \(-885773544457603433627648\) | \([]\) | \(31749120\) | \(3.6271\) | |
179776.y2 | 179776bf1 | \([0, 1, 0, 3771551, 249076735]\) | \(6859/4\) | \(-3460052908037513412608\) | \([]\) | \(6349824\) | \(2.8224\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179776.y have rank \(0\).
Complex multiplication
The elliptic curves in class 179776.y do not have complex multiplication.Modular form 179776.2.a.y
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.