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SageMath
E = EllipticCurve("ie1")
E.isogeny_class()
Elliptic curves in class 433200.ie
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.ie1 | 433200ie2 | \([0, 1, 0, -269008, 32035988]\) | \(4904335099/1822500\) | \(800033760000000000\) | \([2]\) | \(4423680\) | \(2.1352\) | \(\Gamma_0(N)\)-optimal* |
433200.ie2 | 433200ie1 | \([0, 1, 0, -117008, -15084012]\) | \(403583419/10800\) | \(4740940800000000\) | \([2]\) | \(2211840\) | \(1.7886\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200.ie have rank \(1\).
Complex multiplication
The elliptic curves in class 433200.ie do not have complex multiplication.Modular form 433200.2.a.ie
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.