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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 159120.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.o1 | 159120bi1 | \([0, 0, 0, -22158588, -26660395037]\) | \(103157889656032577929216/33372791198022770325\) | \(389260236533737593070800\) | \([2]\) | \(15728640\) | \(3.2299\) | \(\Gamma_0(N)\)-optimal |
159120.o2 | 159120bi2 | \([0, 0, 0, 63167217, -182311728518]\) | \(149359017613560984774704/163373427681970325625\) | \(-30489402567720030049440000\) | \([2]\) | \(31457280\) | \(3.5765\) |
Rank
sage: E.rank()
The elliptic curves in class 159120.o have rank \(0\).
Complex multiplication
The elliptic curves in class 159120.o do not have complex multiplication.Modular form 159120.2.a.o
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.