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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 490.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490.a1 | 490c2 | \([1, 0, 1, -7768, -458202]\) | \(-8990558521/10485760\) | \(-60448319733760\) | \([]\) | \(1764\) | \(1.3385\) | |
490.a2 | 490c1 | \([1, 0, 1, 807, 11708]\) | \(10100279/16000\) | \(-92236816000\) | \([3]\) | \(588\) | \(0.78918\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 490.a have rank \(0\).
Complex multiplication
The elliptic curves in class 490.a do not have complex multiplication.Modular form 490.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.