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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 179776v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179776.h2 | 179776v1 | \([0, 1, 0, 176031, 70019839]\) | \(103823/424\) | \(-2463547816331444224\) | \([]\) | \(3234816\) | \(2.2117\) | \(\Gamma_0(N)\)-optimal |
| 179776.h1 | 179776v2 | \([0, 1, 0, -1621729, -2153809281]\) | \(-81182737/297754\) | \(-1730026454018756706304\) | \([]\) | \(9704448\) | \(2.7610\) |
Rank
sage: E.rank()
The elliptic curves in class 179776v have rank \(1\).
Complex multiplication
The elliptic curves in class 179776v do not have complex multiplication.Modular form 179776.2.a.v
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.
