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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 331056t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
331056.t1 | 331056t1 | \([0, 0, 0, -198965019, -1096552487734]\) | \(-164668416049678897/2902956072984\) | \(-15356210313924043773935616\) | \([]\) | \(91238400\) | \(3.6300\) | \(\Gamma_0(N)\)-optimal |
331056.t2 | 331056t2 | \([0, 0, 0, 774862341, -5227231766614]\) | \(9726437216910146543/7860157321308534\) | \(-41579075222613249340815138816\) | \([]\) | \(273715200\) | \(4.1793\) |
Rank
sage: E.rank()
The elliptic curves in class 331056t have rank \(1\).
Complex multiplication
The elliptic curves in class 331056t do not have complex multiplication.Modular form 331056.2.a.t
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.