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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 162240f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.gt2 | 162240f1 | \([0, 1, 0, -225, -845025]\) | \(-4/975\) | \(-308421510758400\) | \([2]\) | \(516096\) | \(1.4591\) | \(\Gamma_0(N)\)-optimal |
162240.gt1 | 162240f2 | \([0, 1, 0, -135425, -18934785]\) | \(434163602/7605\) | \(4811375567831040\) | \([2]\) | \(1032192\) | \(1.8057\) |
Rank
sage: E.rank()
The elliptic curves in class 162240f have rank \(0\).
Complex multiplication
The elliptic curves in class 162240f do not have complex multiplication.Modular form 162240.2.a.f
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.