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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 317900.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317900.y1 | 317900y1 | \([0, 1, 0, -209498508, 1167065767988]\) | \(-126100646224/605\) | \(-4878705239086580000000\) | \([]\) | \(35956224\) | \(3.3626\) | \(\Gamma_0(N)\)-optimal |
317900.y2 | 317900y2 | \([0, 1, 0, -125977508, 2104672513988]\) | \(-27419122384/221445125\) | \(-1785728085136665444500000000\) | \([]\) | \(107868672\) | \(3.9119\) |
Rank
sage: E.rank()
The elliptic curves in class 317900.y have rank \(1\).
Complex multiplication
The elliptic curves in class 317900.y do not have complex multiplication.Modular form 317900.2.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.