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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 193600.hu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.hu1 | 193600ep2 | \([0, -1, 0, -4321313, 3459015617]\) | \(6352571665/2\) | \(2809644725043200\) | \([]\) | \(3649536\) | \(2.3259\) | |
193600.hu2 | 193600ep1 | \([0, -1, 0, -62113, 3100737]\) | \(18865/8\) | \(11238578900172800\) | \([]\) | \(1216512\) | \(1.7766\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193600.hu have rank \(1\).
Complex multiplication
The elliptic curves in class 193600.hu do not have complex multiplication.Modular form 193600.2.a.hu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.