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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 847.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
847.a1 | 847c2 | \([1, 1, 1, -6234, -177484]\) | \(15124197817/1294139\) | \(2292646180979\) | \([2]\) | \(1440\) | \(1.1129\) | |
847.a2 | 847c1 | \([1, 1, 1, 421, -12440]\) | \(4657463/41503\) | \(-73525096183\) | \([2]\) | \(720\) | \(0.76635\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 847.a have rank \(1\).
Complex multiplication
The elliptic curves in class 847.a do not have complex multiplication.Modular form 847.2.a.a
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.