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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 301392.cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301392.cz1 | 301392cz4 | \([0, 0, 0, -142659, -6139422]\) | \(215062038362754/113550802729\) | \(169530440067975168\) | \([2]\) | \(2293760\) | \(1.9975\) | |
| 301392.cz2 | 301392cz2 | \([0, 0, 0, -81819, 8936730]\) | \(81144432781668/740329681\) | \(552653145547776\) | \([2, 2]\) | \(1146880\) | \(1.6510\) | |
| 301392.cz3 | 301392cz1 | \([0, 0, 0, -81639, 8978310]\) | \(322440248841552/27209\) | \(5077852416\) | \([2]\) | \(573440\) | \(1.3044\) | \(\Gamma_0(N)\)-optimal |
| 301392.cz4 | 301392cz3 | \([0, 0, 0, -23859, 21351762]\) | \(-1006057824354/131332646081\) | \(-196078589937764352\) | \([2]\) | \(2293760\) | \(1.9975\) |
Rank
sage: E.rank()
The elliptic curves in class 301392.cz have rank \(1\).
Complex multiplication
The elliptic curves in class 301392.cz do not have complex multiplication.Modular form 301392.2.a.cz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
