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SageMath
E = EllipticCurve("id1")
E.isogeny_class()
Elliptic curves in class 158400id
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.i2 | 158400id1 | \([0, 0, 0, 28500, -610000]\) | \(34295/22\) | \(-1642291200000000\) | \([]\) | \(829440\) | \(1.6085\) | \(\Gamma_0(N)\)-optimal |
158400.i1 | 158400id2 | \([0, 0, 0, -331500, 85070000]\) | \(-53969305/10648\) | \(-794868940800000000\) | \([]\) | \(2488320\) | \(2.1578\) |
Rank
sage: E.rank()
The elliptic curves in class 158400id have rank \(1\).
Complex multiplication
The elliptic curves in class 158400id do not have complex multiplication.Modular form 158400.2.a.id
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.