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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 118354.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
118354.q1 | 118354m1 | \([1, -1, 1, -4289245, 3420228321]\) | \(206896959473625/236708\) | \(9984469757093828\) | \([2]\) | \(1948800\) | \(2.3544\) | \(\Gamma_0(N)\)-optimal |
118354.q2 | 118354m2 | \([1, -1, 1, -4254435, 3478444565]\) | \(-201900421229625/7003834658\) | \(-295425483407770729778\) | \([2]\) | \(3897600\) | \(2.7010\) |
Rank
sage: E.rank()
The elliptic curves in class 118354.q have rank \(1\).
Complex multiplication
The elliptic curves in class 118354.q do not have complex multiplication.Modular form 118354.2.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.