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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 74529.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74529.e1 | 74529bs2 | \([0, 0, 1, -4792388601, 127695666013438]\) | \(-13383627864961024/151263\) | \(-137574723513925546463979\) | \([]\) | \(59904000\) | \(4.0079\) | |
74529.e2 | 74529bs1 | \([0, 0, 1, 3552549, 29386819894]\) | \(5451776/413343\) | \(-375938259464750316680619\) | \([]\) | \(11980800\) | \(3.2032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74529.e have rank \(0\).
Complex multiplication
The elliptic curves in class 74529.e do not have complex multiplication.Modular form 74529.2.a.e
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.