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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 363888f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
363888.f1 | 363888f1 | \([0, 0, 0, -17499, -1507574]\) | \(-549754417/592704\) | \(-638899482525696\) | \([]\) | \(1244160\) | \(1.5358\) | \(\Gamma_0(N)\)-optimal |
363888.f2 | 363888f2 | \([0, 0, 0, 146661, 27220426]\) | \(323648023823/484243284\) | \(-521985314025455616\) | \([]\) | \(3732480\) | \(2.0851\) |
Rank
sage: E.rank()
The elliptic curves in class 363888f have rank \(0\).
Complex multiplication
The elliptic curves in class 363888f do not have complex multiplication.Modular form 363888.2.a.f
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.