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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 180336.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180336.s1 | 180336cu2 | \([0, -1, 0, -94888, -10416320]\) | \(3822686500/304317\) | \(7521763927421952\) | \([2]\) | \(1179648\) | \(1.7899\) | |
180336.s2 | 180336cu1 | \([0, -1, 0, -19748, 884736]\) | \(137842000/25857\) | \(159776031138048\) | \([2]\) | \(589824\) | \(1.4433\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180336.s have rank \(1\).
Complex multiplication
The elliptic curves in class 180336.s do not have complex multiplication.Modular form 180336.2.a.s
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.