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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 176400p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.ea2 | 176400p1 | \([0, 0, 0, 294000, 85750000]\) | \(4096/7\) | \(-4802902776000000000\) | \([]\) | \(2304000\) | \(2.2696\) | \(\Gamma_0(N)\)-optimal |
| 176400.ea1 | 176400p2 | \([0, 0, 0, -26166000, -51775850000]\) | \(-2887553024/16807\) | \(-11531769565176000000000\) | \([]\) | \(11520000\) | \(3.0743\) |
Rank
sage: E.rank()
The elliptic curves in class 176400p have rank \(1\).
Complex multiplication
The elliptic curves in class 176400p do not have complex multiplication.Modular form 176400.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
