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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 79402.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79402.a1 | 79402d2 | \([1, 1, 0, -622923, -190777151]\) | \(-10418796526321/82044596\) | \(-210503986672935764\) | \([]\) | \(993600\) | \(2.1526\) | |
79402.a2 | 79402d1 | \([1, 1, 0, 6817, 362629]\) | \(13651919/29696\) | \(-76191811441664\) | \([]\) | \(198720\) | \(1.3479\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79402.a have rank \(2\).
Complex multiplication
The elliptic curves in class 79402.a do not have complex multiplication.Modular form 79402.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.