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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 180336.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180336.q1 | 180336bh2 | \([0, -1, 0, -82205568, -286849880064]\) | \(621403856941038625/6310317312\) | \(623885187196086386688\) | \([2]\) | \(14155776\) | \(3.1487\) | |
180336.q2 | 180336bh1 | \([0, -1, 0, -5262208, -4252307456]\) | \(162995025390625/15251079168\) | \(1507835804639488376832\) | \([2]\) | \(7077888\) | \(2.8022\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180336.q have rank \(0\).
Complex multiplication
The elliptic curves in class 180336.q do not have complex multiplication.Modular form 180336.2.a.q
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.