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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 227154p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227154.g4 | 227154p1 | \([1, 0, 1, -8532, 44626]\) | \(2845178713/1609728\) | \(38854920671232\) | \([2]\) | \(737280\) | \(1.2976\) | \(\Gamma_0(N)\)-optimal |
227154.g2 | 227154p2 | \([1, 0, 1, -101012, 12325970]\) | \(4722184089433/9884736\) | \(238593497246784\) | \([2, 2]\) | \(1474560\) | \(1.6441\) | |
227154.g1 | 227154p3 | \([1, 0, 1, -1615372, 790101266]\) | \(19312898130234073/84888\) | \(2048989957272\) | \([2]\) | \(2949120\) | \(1.9907\) | |
227154.g3 | 227154p4 | \([1, 0, 1, -66332, 20926610]\) | \(-1337180541913/7067998104\) | \(-170604291927169176\) | \([2]\) | \(2949120\) | \(1.9907\) |
Rank
sage: E.rank()
The elliptic curves in class 227154p have rank \(0\).
Complex multiplication
The elliptic curves in class 227154p do not have complex multiplication.Modular form 227154.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.