Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 3024.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3024.y1 | 3024x2 | \([0, 0, 0, -6816, -216592]\) | \(35184082944/7\) | \(6967296\) | \([]\) | \(2592\) | \(0.70248\) | |
3024.y2 | 3024x3 | \([0, 0, 0, -3456, 78192]\) | \(56623104/7\) | \(564350976\) | \([]\) | \(2592\) | \(0.70248\) | |
3024.y3 | 3024x1 | \([0, 0, 0, -96, -208]\) | \(884736/343\) | \(37933056\) | \([]\) | \(864\) | \(0.15317\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3024.y have rank \(1\).
Complex multiplication
The elliptic curves in class 3024.y do not have complex multiplication.Modular form 3024.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.