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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 11830f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11830.m2 | 11830f1 | \([1, 0, 1, 412, 12898]\) | \(45924354671/449576960\) | \(-75978506240\) | \([]\) | \(10368\) | \(0.76896\) | \(\Gamma_0(N)\)-optimal |
11830.m1 | 11830f2 | \([1, 0, 1, -3748, -366494]\) | \(-34440478374289/322828856000\) | \(-54558076664000\) | \([]\) | \(31104\) | \(1.3183\) |
Rank
sage: E.rank()
The elliptic curves in class 11830f have rank \(0\).
Complex multiplication
The elliptic curves in class 11830f do not have complex multiplication.Modular form 11830.2.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.