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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 129430.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129430.j1 | 129430c2 | \([1, 0, 1, -17602519, -59903937158]\) | \(-51606035560969/102760448000\) | \(-1201084696840003125248000\) | \([]\) | \(20805120\) | \(3.3099\) | |
129430.j2 | 129430c1 | \([1, 0, 1, 1876696, 1759465846]\) | \(62540044391/150590720\) | \(-1760134495308134462720\) | \([3]\) | \(6935040\) | \(2.7606\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129430.j have rank \(0\).
Complex multiplication
The elliptic curves in class 129430.j do not have complex multiplication.Modular form 129430.2.a.j
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.