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SageMath
E = EllipticCurve("jp1")
E.isogeny_class()
Elliptic curves in class 433200jp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
433200.jp2 | 433200jp1 | \([0, 1, 0, -32637408, -73904092812]\) | \(-186169411/6480\) | \(-133825042022906880000000\) | \([2]\) | \(42024960\) | \(3.2105\) | \(\Gamma_0(N)\)-optimal* |
433200.jp1 | 433200jp2 | \([0, 1, 0, -526485408, -4649899660812]\) | \(781484460931/900\) | \(18586811392070400000000\) | \([2]\) | \(84049920\) | \(3.5571\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 433200jp have rank \(1\).
Complex multiplication
The elliptic curves in class 433200jp do not have complex multiplication.Modular form 433200.2.a.jp
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.