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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 480960.eg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
480960.eg1 | 480960eg2 | \([0, 0, 0, -64654572, -199931663536]\) | \(156406207396688718841/152178750000000\) | \(29081812008960000000000\) | \([2]\) | \(46448640\) | \(3.2311\) | \(\Gamma_0(N)\)-optimal* |
480960.eg2 | 480960eg1 | \([0, 0, 0, -3091692, -4629583024]\) | \(-17101922279625721/38553753600000\) | \(-7367737048930713600000\) | \([2]\) | \(23224320\) | \(2.8845\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 480960.eg have rank \(0\).
Complex multiplication
The elliptic curves in class 480960.eg do not have complex multiplication.Modular form 480960.2.a.eg
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.