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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 16184f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16184.e1 | 16184f1 | \([0, -1, 0, -232, 1212]\) | \(275684/49\) | \(246514688\) | \([2]\) | \(5120\) | \(0.32965\) | \(\Gamma_0(N)\)-optimal |
16184.e2 | 16184f2 | \([0, -1, 0, 448, 6380]\) | \(986078/2401\) | \(-24158439424\) | \([2]\) | \(10240\) | \(0.67622\) |
Rank
sage: E.rank()
The elliptic curves in class 16184f have rank \(1\).
Complex multiplication
The elliptic curves in class 16184f do not have complex multiplication.Modular form 16184.2.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.