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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 72324f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72324.u1 | 72324f1 | \([0, 0, 0, -19551, -1099658]\) | \(-768208/41\) | \(-44109859094784\) | \([]\) | \(241920\) | \(1.3771\) | \(\Gamma_0(N)\)-optimal |
72324.u2 | 72324f2 | \([0, 0, 0, 103929, -2309762]\) | \(115393712/68921\) | \(-74148673138331904\) | \([3]\) | \(725760\) | \(1.9264\) |
Rank
sage: E.rank()
The elliptic curves in class 72324f have rank \(0\).
Complex multiplication
The elliptic curves in class 72324f do not have complex multiplication.Modular form 72324.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.