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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 66150db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66150.da3 | 66150db1 | \([1, -1, 0, 12633, -339459]\) | \(4492125/3584\) | \(-177885288000000\) | \([]\) | \(248832\) | \(1.4223\) | \(\Gamma_0(N)\)-optimal |
66150.da2 | 66150db2 | \([1, -1, 0, -134367, 24307541]\) | \(-7414875/2744\) | \(-99285005822625000\) | \([]\) | \(746496\) | \(1.9716\) | |
66150.da1 | 66150db3 | \([1, -1, 0, -11710617, 15427665791]\) | \(-545407363875/14\) | \(-4559005369406250\) | \([]\) | \(2239488\) | \(2.5209\) |
Rank
sage: E.rank()
The elliptic curves in class 66150db have rank \(1\).
Complex multiplication
The elliptic curves in class 66150db do not have complex multiplication.Modular form 66150.2.a.db
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.