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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 394944u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
394944.u2 | 394944u1 | \([0, -1, 0, -3188878689, -66620520833535]\) | \(7722211175253055152433/340131399900069888\) | \(157958412157155465194417160192\) | \([2]\) | \(373800960\) | \(4.3658\) | \(\Gamma_0(N)\)-optimal |
394944.u1 | 394944u2 | \([0, -1, 0, -8581180769, 218102735134209]\) | \(150476552140919246594353/42832838728685592576\) | \(19891745354161580164915170115584\) | \([2]\) | \(747601920\) | \(4.7123\) |
Rank
sage: E.rank()
The elliptic curves in class 394944u have rank \(1\).
Complex multiplication
The elliptic curves in class 394944u do not have complex multiplication.Modular form 394944.2.a.u
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 Cremona 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 Cremona labels.