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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 27720i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27720.v1 | 27720i1 | \([0, 0, 0, -1083, -13498]\) | \(188183524/3465\) | \(2586608640\) | \([2]\) | \(18432\) | \(0.60076\) | \(\Gamma_0(N)\)-optimal |
27720.v2 | 27720i2 | \([0, 0, 0, -3, -39202]\) | \(-2/444675\) | \(-663896217600\) | \([2]\) | \(36864\) | \(0.94733\) |
Rank
sage: E.rank()
The elliptic curves in class 27720i have rank \(0\).
Complex multiplication
The elliptic curves in class 27720i do not have complex multiplication.Modular form 27720.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.