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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4368.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4368.e1 | 4368n2 | \([0, -1, 0, -58791936, 173529697152]\) | \(-5486773802537974663600129/2635437714\) | \(-10794752876544\) | \([]\) | \(197568\) | \(2.7397\) | |
4368.e2 | 4368n1 | \([0, -1, 0, 11424, 5306112]\) | \(40251338884511/2997011332224\) | \(-12275758416789504\) | \([]\) | \(28224\) | \(1.7667\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4368.e have rank \(0\).
Complex multiplication
The elliptic curves in class 4368.e do not have complex multiplication.Modular form 4368.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.