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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 28224.ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28224.ff1 | 28224fq2 | \([0, 0, 0, -32844, 2292878]\) | \(-1713910976512/1594323\) | \(-3644851960512\) | \([]\) | \(49920\) | \(1.3333\) | |
28224.ff2 | 28224fq1 | \([0, 0, 0, -84, -322]\) | \(-28672/3\) | \(-6858432\) | \([]\) | \(3840\) | \(0.050792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28224.ff have rank \(0\).
Complex multiplication
The elliptic curves in class 28224.ff do not have complex multiplication.Modular form 28224.2.a.ff
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.