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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 67158.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67158.y1 | 67158y2 | \([1, -1, 0, -24477301773, 1473992350953957]\) | \(-2224778660867235879101476628566993/16157901081011429376\) | \(-11779109888057332015104\) | \([3]\) | \(75209472\) | \(4.2876\) | |
| 67158.y2 | 67158y1 | \([1, -1, 0, -300784653, 2041726210533]\) | \(-4128223528775369483123266513/81108488685750967074816\) | \(-59128088251912454997540864\) | \([]\) | \(25069824\) | \(3.7383\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67158.y have rank \(1\).
Complex multiplication
The elliptic curves in class 67158.y do not have complex multiplication.Modular form 67158.2.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.
