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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 254320w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254320.w2 | 254320w1 | \([0, 0, 0, -653090003, 6288242803602]\) | \(63422386460383257/1535220121600\) | \(745711592144937459856179200\) | \([2]\) | \(91914240\) | \(3.9408\) | \(\Gamma_0(N)\)-optimal |
254320.w1 | 254320w2 | \([0, 0, 0, -1458035923, -12275580992622]\) | \(705713043507894297/274379367680000\) | \(133275920661548209835868160000\) | \([2]\) | \(183828480\) | \(4.2873\) |
Rank
sage: E.rank()
The elliptic curves in class 254320w have rank \(0\).
Complex multiplication
The elliptic curves in class 254320w do not have complex multiplication.Modular form 254320.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.