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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 179776.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179776.n1 | 179776f2 | \([0, -1, 0, -34273, 2453633]\) | \(-6046458625/2\) | \(-1472724992\) | \([]\) | \(186624\) | \(1.1178\) | |
179776.n2 | 179776f1 | \([0, -1, 0, -353, 4609]\) | \(-6625/8\) | \(-5890899968\) | \([]\) | \(62208\) | \(0.56845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179776.n have rank \(2\).
Complex multiplication
The elliptic curves in class 179776.n do not have complex multiplication.Modular form 179776.2.a.n
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.