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SageMath
E = EllipticCurve("sg1")
E.isogeny_class()
Elliptic curves in class 310464sg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.sg2 | 310464sg1 | \([0, 0, 0, -176988, 30924880]\) | \(-1272112/121\) | \(-58319688824635392\) | \([2]\) | \(4128768\) | \(1.9587\) | \(\Gamma_0(N)\)-optimal |
310464.sg1 | 310464sg2 | \([0, 0, 0, -2893548, 1894485040]\) | \(1389715708/11\) | \(21207159572594688\) | \([2]\) | \(8257536\) | \(2.3053\) |
Rank
sage: E.rank()
The elliptic curves in class 310464sg have rank \(0\).
Complex multiplication
The elliptic curves in class 310464sg do not have complex multiplication.Modular form 310464.2.a.sg
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.