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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 436800.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.w1 | 436800w2 | \([0, -1, 0, -962913, 308266497]\) | \(3013251478061453/493573702986\) | \(16173423099445248000\) | \([2]\) | \(11501568\) | \(2.4075\) | |
436800.w2 | 436800w1 | \([0, -1, 0, -921313, 340672897]\) | \(2639343078571373/93139956\) | \(3052010078208000\) | \([2]\) | \(5750784\) | \(2.0610\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 436800.w have rank \(1\).
Complex multiplication
The elliptic curves in class 436800.w do not have complex multiplication.Modular form 436800.2.a.w
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 LMFDB 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 LMFDB labels.