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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 426a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426.c2 | 426a1 | \([1, 0, 0, -20, 48]\) | \(-887503681/552096\) | \(-552096\) | \([5]\) | \(80\) | \(-0.19647\) | \(\Gamma_0(N)\)-optimal |
426.c1 | 426a2 | \([1, 0, 0, -230, -5202]\) | \(-1345938541921/10825376106\) | \(-10825376106\) | \([]\) | \(400\) | \(0.60825\) |
Rank
sage: E.rank()
The elliptic curves in class 426a have rank \(0\).
Complex multiplication
The elliptic curves in class 426a do not have complex multiplication.Modular form 426.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.