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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 26010i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.j1 | 26010i1 | \([1, -1, 0, -360, -3200]\) | \(-24529249/8000\) | \(-1685448000\) | \([]\) | \(12960\) | \(0.48296\) | \(\Gamma_0(N)\)-optimal |
26010.j2 | 26010i2 | \([1, -1, 0, 2700, 29236]\) | \(10329972191/7812500\) | \(-1645945312500\) | \([]\) | \(38880\) | \(1.0323\) |
Rank
sage: E.rank()
The elliptic curves in class 26010i have rank \(0\).
Complex multiplication
The elliptic curves in class 26010i do not have complex multiplication.Modular form 26010.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.