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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 19845a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19845.g2 | 19845a1 | \([0, 0, 1, -588, -5231]\) | \(2359296/125\) | \(1191196125\) | \([]\) | \(8640\) | \(0.49832\) | \(\Gamma_0(N)\)-optimal |
19845.g1 | 19845a2 | \([0, 0, 1, -7938, 270884]\) | \(884736/5\) | \(312617511045\) | \([]\) | \(25920\) | \(1.0476\) |
Rank
sage: E.rank()
The elliptic curves in class 19845a have rank \(0\).
Complex multiplication
The elliptic curves in class 19845a do not have complex multiplication.Modular form 19845.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.