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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 107800q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
107800.ch2 | 107800q1 | \([0, -1, 0, -2508, 53012]\) | \(-1272112/121\) | \(-166012000000\) | \([2]\) | \(122880\) | \(0.89463\) | \(\Gamma_0(N)\)-optimal |
107800.ch1 | 107800q2 | \([0, -1, 0, -41008, 3210012]\) | \(1389715708/11\) | \(60368000000\) | \([2]\) | \(245760\) | \(1.2412\) |
Rank
sage: E.rank()
The elliptic curves in class 107800q have rank \(1\).
Complex multiplication
The elliptic curves in class 107800q do not have complex multiplication.Modular form 107800.2.a.q
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.