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SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 117600.ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117600.ea1 | 117600bd2 | \([0, -1, 0, -24033, -1422063]\) | \(69934528/225\) | \(4939200000000\) | \([2]\) | \(393216\) | \(1.3019\) | |
117600.ea2 | 117600bd1 | \([0, -1, 0, -2158, -188]\) | \(3241792/1875\) | \(643125000000\) | \([2]\) | \(196608\) | \(0.95528\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117600.ea have rank \(0\).
Complex multiplication
The elliptic curves in class 117600.ea do not have complex multiplication.Modular form 117600.2.a.ea
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.