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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 155526cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155526.h3 | 155526cy1 | \([1, 1, 0, -920735, 355219509]\) | \(-4956477625/268272\) | \(-4672298740340497392\) | \([2]\) | \(3041280\) | \(2.3408\) | \(\Gamma_0(N)\)-optimal |
155526.h2 | 155526cy2 | \([1, 1, 0, -14918075, 22171473633]\) | \(21081759765625/57132\) | \(995026583591031852\) | \([2]\) | \(6082560\) | \(2.6874\) | |
155526.h4 | 155526cy3 | \([1, 1, 0, 4911490, 730114932]\) | \(752329532375/448524288\) | \(-7811622032245327392768\) | \([2]\) | \(9123840\) | \(2.8901\) | |
155526.h1 | 155526cy4 | \([1, 1, 0, -19972670, 5861228724]\) | \(50591419971625/28422890688\) | \(495020860762129679103168\) | \([2]\) | \(18247680\) | \(3.2367\) |
Rank
sage: E.rank()
The elliptic curves in class 155526cy have rank \(1\).
Complex multiplication
The elliptic curves in class 155526cy do not have complex multiplication.Modular form 155526.2.a.cy
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.