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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 435344.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.m1 | 435344m2 | \([0, 1, 0, -37912, 2374932]\) | \(304821217/51842\) | \(1024947946201088\) | \([2]\) | \(2488320\) | \(1.6009\) | \(\Gamma_0(N)\)-optimal* |
435344.m2 | 435344m1 | \([0, 1, 0, -10872, -404780]\) | \(7189057/644\) | \(12732272623616\) | \([2]\) | \(1244160\) | \(1.2544\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.m have rank \(1\).
Complex multiplication
The elliptic curves in class 435344.m do not have complex multiplication.Modular form 435344.2.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.