Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 279312.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279312.y1 | 279312y2 | \([0, -1, 0, -750298, 250376131]\) | \(37280608000/3993\) | \(5003132227632528\) | \([]\) | \(2861568\) | \(2.0431\) | |
279312.y2 | 279312y1 | \([0, -1, 0, -20278, -604745]\) | \(736000/297\) | \(372133802055312\) | \([]\) | \(953856\) | \(1.4938\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 279312.y have rank \(0\).
Complex multiplication
The elliptic curves in class 279312.y do not have complex multiplication.Modular form 279312.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.