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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 430950.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.e1 | 430950e2 | \([1, 1, 0, -30930, 1980750]\) | \(5423945093/293046\) | \(176809633776750\) | \([2]\) | \(2408448\) | \(1.4900\) | \(\Gamma_0(N)\)-optimal* |
430950.e2 | 430950e1 | \([1, 1, 0, -5580, -123300]\) | \(31855013/7956\) | \(4800261550500\) | \([2]\) | \(1204224\) | \(1.1434\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.e have rank \(1\).
Complex multiplication
The elliptic curves in class 430950.e do not have complex multiplication.Modular form 430950.2.a.e
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.