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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 439824o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439824.o2 | 439824o1 | \([0, -1, 0, -322841024, -2145948288000]\) | \(7722211175253055152433/340131399900069888\) | \(163906023697790247949565952\) | \([2]\) | \(140175360\) | \(3.7932\) | \(\Gamma_0(N)\)-optimal* |
439824.o1 | 439824o2 | \([0, -1, 0, -868755904, 7025858427904]\) | \(150476552140919246594353/42832838728685592576\) | \(20640729676149273726868783104\) | \([2]\) | \(280350720\) | \(4.1398\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439824o have rank \(1\).
Complex multiplication
The elliptic curves in class 439824o do not have complex multiplication.Modular form 439824.2.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 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.