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SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 405600.gr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.gr1 | 405600gr2 | \([0, 1, 0, -9740033, 10502970063]\) | \(150568768/16875\) | \(11452859322840000000000\) | \([2]\) | \(40255488\) | \(2.9656\) | \(\Gamma_0(N)\)-optimal* |
405600.gr2 | 405600gr1 | \([0, 1, 0, -2325158, -1190287812]\) | \(131096512/18225\) | \(193267001072925000000\) | \([2]\) | \(20127744\) | \(2.6190\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 405600.gr have rank \(0\).
Complex multiplication
The elliptic curves in class 405600.gr do not have complex multiplication.Modular form 405600.2.a.gr
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.