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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 237160co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
237160.co2 | 237160co1 | \([0, -1, 0, 180, -21580]\) | \(16/5\) | \(-200436248320\) | \([2]\) | \(221184\) | \(0.84779\) | \(\Gamma_0(N)\)-optimal |
237160.co1 | 237160co2 | \([0, -1, 0, -10600, -405348]\) | \(821516/25\) | \(4008724966400\) | \([2]\) | \(442368\) | \(1.1944\) |
Rank
sage: E.rank()
The elliptic curves in class 237160co have rank \(1\).
Complex multiplication
The elliptic curves in class 237160co do not have complex multiplication.Modular form 237160.2.a.co
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.