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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 38025p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.bc2 | 38025p1 | \([1, -1, 1, 1645, -196478]\) | \(729/25\) | \(-16892012109375\) | \([2]\) | \(82944\) | \(1.2181\) | \(\Gamma_0(N)\)-optimal |
38025.bc1 | 38025p2 | \([1, -1, 1, -42230, -3179978]\) | \(12326391/625\) | \(422300302734375\) | \([2]\) | \(165888\) | \(1.5647\) |
Rank
sage: E.rank()
The elliptic curves in class 38025p have rank \(0\).
Complex multiplication
The elliptic curves in class 38025p do not have complex multiplication.Modular form 38025.2.a.p
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.