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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 59840.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
59840.i1 | 59840bm1 | \([0, 1, 0, -1045, -14157]\) | \(-7710244864/565675\) | \(-9268019200\) | \([]\) | \(50688\) | \(0.66166\) | \(\Gamma_0(N)\)-optimal |
59840.i2 | 59840bm2 | \([0, 1, 0, 5995, -8525]\) | \(1454115454976/844421875\) | \(-13835008000000\) | \([]\) | \(152064\) | \(1.2110\) |
Rank
sage: E.rank()
The elliptic curves in class 59840.i have rank \(0\).
Complex multiplication
The elliptic curves in class 59840.i do not have complex multiplication.Modular form 59840.2.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 LMFDB 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 LMFDB labels.