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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 50094.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50094.q1 | 50094a1 | \([1, -1, 0, -4197, -194067]\) | \(-170953875/244904\) | \(-11714284128888\) | \([]\) | \(103680\) | \(1.1998\) | \(\Gamma_0(N)\)-optimal |
50094.q2 | 50094a2 | \([1, -1, 0, 35733, 3844187]\) | \(144703125/267674\) | \(-9333694722620862\) | \([]\) | \(311040\) | \(1.7491\) |
Rank
sage: E.rank()
The elliptic curves in class 50094.q have rank \(0\).
Complex multiplication
The elliptic curves in class 50094.q do not have complex multiplication.Modular form 50094.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.