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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 36300.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36300.k1 | 36300o1 | \([0, -1, 0, -321658, 73244437]\) | \(-68679424/3375\) | \(-180865305843750000\) | \([]\) | \(342144\) | \(2.0729\) | \(\Gamma_0(N)\)-optimal |
36300.k2 | 36300o2 | \([0, -1, 0, 1674842, 175065937]\) | \(9695350016/5859375\) | \(-314002267089843750000\) | \([]\) | \(1026432\) | \(2.6222\) |
Rank
sage: E.rank()
The elliptic curves in class 36300.k have rank \(1\).
Complex multiplication
The elliptic curves in class 36300.k do not have complex multiplication.Modular form 36300.2.a.k
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.