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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 88935.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.n1 | 88935o4 | \([1, 1, 1, -3409278881, 76618536312044]\) | \(21026497979043461623321/161783881875\) | \(33719381720425127986875\) | \([2]\) | \(44236800\) | \(3.9152\) | |
88935.n2 | 88935o2 | \([1, 1, 1, -213221786, 1195424138558]\) | \(5143681768032498601/14238434358225\) | \(2967608377682247733382025\) | \([2, 2]\) | \(22118400\) | \(3.5686\) | |
88935.n3 | 88935o3 | \([1, 1, 1, -129178211, 2147503373588]\) | \(-1143792273008057401/8897444448004035\) | \(-1854426548562659780175659115\) | \([2]\) | \(44236800\) | \(3.9152\) | |
88935.n4 | 88935o1 | \([1, 1, 1, -18720941, 2122554314]\) | \(3481467828171481/2005331497785\) | \(417955963635788931602865\) | \([2]\) | \(11059200\) | \(3.2220\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88935.n have rank \(1\).
Complex multiplication
The elliptic curves in class 88935.n do not have complex multiplication.Modular form 88935.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.