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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 135531i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
135531.d2 | 135531i1 | \([1, -1, 1, -20792, 218890]\) | \(19683/11\) | \(555513121991817\) | \([2]\) | \(608256\) | \(1.5195\) | \(\Gamma_0(N)\)-optimal |
135531.d1 | 135531i2 | \([1, -1, 1, -205607, -35635220]\) | \(19034163/121\) | \(6110644341909987\) | \([2]\) | \(1216512\) | \(1.8661\) |
Rank
sage: E.rank()
The elliptic curves in class 135531i have rank \(0\).
Complex multiplication
The elliptic curves in class 135531i do not have complex multiplication.Modular form 135531.2.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.