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SageMath
E = EllipticCurve("it1")
E.isogeny_class()
Elliptic curves in class 177870it
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177870.z2 | 177870it1 | \([1, 1, 0, 118457, -68277887]\) | \(2571353/29700\) | \(-2123219628204651900\) | \([2]\) | \(4515840\) | \(2.1976\) | \(\Gamma_0(N)\)-optimal |
177870.z1 | 177870it2 | \([1, 1, 0, -1956693, -982588977]\) | \(11589205447/882090\) | \(63059622957678161430\) | \([2]\) | \(9031680\) | \(2.5441\) |
Rank
sage: E.rank()
The elliptic curves in class 177870it have rank \(1\).
Complex multiplication
The elliptic curves in class 177870it do not have complex multiplication.Modular form 177870.2.a.it
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.