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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2320f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2320.e1 | 2320f1 | \([0, 0, 0, -43, -102]\) | \(2146689/145\) | \(593920\) | \([2]\) | \(256\) | \(-0.14335\) | \(\Gamma_0(N)\)-optimal |
2320.e2 | 2320f2 | \([0, 0, 0, 37, -438]\) | \(1367631/21025\) | \(-86118400\) | \([2]\) | \(512\) | \(0.20322\) |
Rank
sage: E.rank()
The elliptic curves in class 2320f have rank \(0\).
Complex multiplication
The elliptic curves in class 2320f do not have complex multiplication.Modular form 2320.2.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.