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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 39039e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39039.h1 | 39039e1 | \([1, 1, 1, -231, 996]\) | \(620650477/124509\) | \(273546273\) | \([2]\) | \(25920\) | \(0.33495\) | \(\Gamma_0(N)\)-optimal |
39039.h2 | 39039e2 | \([1, 1, 1, 484, 6716]\) | \(5706550403/11647251\) | \(-25589010447\) | \([2]\) | \(51840\) | \(0.68152\) |
Rank
sage: E.rank()
The elliptic curves in class 39039e have rank \(0\).
Complex multiplication
The elliptic curves in class 39039e do not have complex multiplication.Modular form 39039.2.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 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.