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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 129360.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.i1 | 129360dw2 | \([0, -1, 0, -23816, 1422576]\) | \(1063394339743/43560\) | \(61198663680\) | \([2]\) | \(184320\) | \(1.1515\) | |
129360.i2 | 129360dw1 | \([0, -1, 0, -1416, 24816]\) | \(-223648543/52800\) | \(-74180198400\) | \([2]\) | \(92160\) | \(0.80490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.i have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.i do not have complex multiplication.Modular form 129360.2.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 LMFDB 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 LMFDB labels.