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SageMath
E = EllipticCurve("fw1")
E.isogeny_class()
Elliptic curves in class 129600fw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129600.hh2 | 129600fw1 | \([0, 0, 0, -1200, -15250]\) | \(2359296/125\) | \(10125000000\) | \([]\) | \(82944\) | \(0.67666\) | \(\Gamma_0(N)\)-optimal |
129600.hh1 | 129600fw2 | \([0, 0, 0, -16200, 789750]\) | \(884736/5\) | \(2657205000000\) | \([]\) | \(248832\) | \(1.2260\) |
Rank
sage: E.rank()
The elliptic curves in class 129600fw have rank \(0\).
Complex multiplication
The elliptic curves in class 129600fw do not have complex multiplication.Modular form 129600.2.a.fw
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.