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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 224400et
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.bf2 | 224400et1 | \([0, -1, 0, -164714808, 782145248112]\) | \(7722211175253055152433/340131399900069888\) | \(21768409593604472832000000\) | \([2]\) | \(49840128\) | \(3.6250\) | \(\Gamma_0(N)\)-optimal |
224400.bf1 | 224400et2 | \([0, -1, 0, -443242808, -2560190751888]\) | \(150476552140919246594353/42832838728685592576\) | \(2741301678635877924864000000\) | \([2]\) | \(99680256\) | \(3.9715\) |
Rank
sage: E.rank()
The elliptic curves in class 224400et have rank \(0\).
Complex multiplication
The elliptic curves in class 224400et do not have complex multiplication.Modular form 224400.2.a.et
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.