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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 262080d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.d1 | 262080d1 | \([0, 0, 0, -167268, 26104192]\) | \(173330435521216/1720616625\) | \(5137733712384000\) | \([2]\) | \(2064384\) | \(1.8334\) | \(\Gamma_0(N)\)-optimal |
262080.d2 | 262080d2 | \([0, 0, 0, -43788, 63790288]\) | \(-388697347592/73364484375\) | \(-1752521412096000000\) | \([2]\) | \(4128768\) | \(2.1799\) |
Rank
sage: E.rank()
The elliptic curves in class 262080d have rank \(1\).
Complex multiplication
The elliptic curves in class 262080d do not have complex multiplication.Modular form 262080.2.a.d
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.