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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 54390n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54390.m2 | 54390n1 | \([1, 1, 0, 6198, 515124]\) | \(223759095911/1094104800\) | \(-128720335615200\) | \([]\) | \(272160\) | \(1.3897\) | \(\Gamma_0(N)\)-optimal |
54390.m1 | 54390n2 | \([1, 1, 0, -347337, 78744261]\) | \(-39390416456458249/56832000000\) | \(-6686227968000000\) | \([]\) | \(816480\) | \(1.9390\) |
Rank
sage: E.rank()
The elliptic curves in class 54390n have rank \(0\).
Complex multiplication
The elliptic curves in class 54390n do not have complex multiplication.Modular form 54390.2.a.n
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.