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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 180336co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
180336.b1 | 180336co1 | \([0, -1, 0, -188235, -29468934]\) | \(1909913257984/129730653\) | \(50102121411240912\) | \([2]\) | \(2457600\) | \(1.9530\) | \(\Gamma_0(N)\)-optimal |
180336.b2 | 180336co2 | \([0, -1, 0, 162900, -127084464]\) | \(77366117936/1172914587\) | \(-7247694534353664768\) | \([2]\) | \(4915200\) | \(2.2996\) |
Rank
sage: E.rank()
The elliptic curves in class 180336co have rank \(1\).
Complex multiplication
The elliptic curves in class 180336co do not have complex multiplication.Modular form 180336.2.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.