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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 30030.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30030.m1 | 30030n2 | \([1, 0, 1, -23544, -423674]\) | \(1443237959152894969/758379911889600\) | \(758379911889600\) | \([2]\) | \(172032\) | \(1.5469\) | |
30030.m2 | 30030n1 | \([1, 0, 1, 5576, -50938]\) | \(19178028702152711/12239832084480\) | \(-12239832084480\) | \([2]\) | \(86016\) | \(1.2003\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30030.m have rank \(1\).
Complex multiplication
The elliptic curves in class 30030.m do not have complex multiplication.Modular form 30030.2.a.m
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.