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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7600.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7600.n1 | 7600l3 | \([0, 1, 0, -34208, 19577588]\) | \(-69173457625/2550136832\) | \(-163208757248000000\) | \([]\) | \(62208\) | \(1.9830\) | |
| 7600.n2 | 7600l1 | \([0, 1, 0, -6208, -190412]\) | \(-413493625/152\) | \(-9728000000\) | \([]\) | \(6912\) | \(0.88442\) | \(\Gamma_0(N)\)-optimal |
| 7600.n3 | 7600l2 | \([0, 1, 0, 3792, -714412]\) | \(94196375/3511808\) | \(-224755712000000\) | \([]\) | \(20736\) | \(1.4337\) |
Rank
sage: E.rank()
The elliptic curves in class 7600.n have rank \(0\).
Complex multiplication
The elliptic curves in class 7600.n do not have complex multiplication.Modular form 7600.2.a.n
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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
