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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 10608i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10608.m2 | 10608i1 | \([0, 1, 0, -55, -136]\) | \(1171019776/304317\) | \(4869072\) | \([2]\) | \(2048\) | \(-0.0077443\) | \(\Gamma_0(N)\)-optimal |
10608.m1 | 10608i2 | \([0, 1, 0, -820, -9316]\) | \(238481570896/25857\) | \(6619392\) | \([2]\) | \(4096\) | \(0.33883\) |
Rank
sage: E.rank()
The elliptic curves in class 10608i have rank \(1\).
Complex multiplication
The elliptic curves in class 10608i do not have complex multiplication.Modular form 10608.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.