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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 177870.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177870.q1 | 177870ix1 | \([1, 1, 0, -67498, -6775292]\) | \(217190179331/97200\) | \(15220627606800\) | \([2]\) | \(691200\) | \(1.4876\) | \(\Gamma_0(N)\)-optimal |
177870.q2 | 177870ix2 | \([1, 1, 0, -56718, -8998128]\) | \(-128864147651/147622500\) | \(-23116328177827500\) | \([2]\) | \(1382400\) | \(1.8342\) |
Rank
sage: E.rank()
The elliptic curves in class 177870.q have rank \(0\).
Complex multiplication
The elliptic curves in class 177870.q do not have complex multiplication.Modular form 177870.2.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 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.