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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 35280eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.e2 | 35280eu1 | \([0, 0, 0, 357, -182]\) | \(34391/20\) | \(-2926264320\) | \([]\) | \(17280\) | \(0.50586\) | \(\Gamma_0(N)\)-optimal |
35280.e1 | 35280eu2 | \([0, 0, 0, -4683, 133882]\) | \(-77626969/8000\) | \(-1170505728000\) | \([]\) | \(51840\) | \(1.0552\) |
Rank
sage: E.rank()
The elliptic curves in class 35280eu have rank \(0\).
Complex multiplication
The elliptic curves in class 35280eu do not have complex multiplication.Modular form 35280.2.a.eu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.