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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 348816.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348816.n1 | 348816n2 | \([0, -1, 0, -161972360, 793579632624]\) | \(-23769846831649063249/3261823333284\) | \(-64488235915285343256576\) | \([]\) | \(49787136\) | \(3.3945\) | |
| 348816.n2 | 348816n1 | \([0, -1, 0, 429880, -242516496]\) | \(444369620591/1540767744\) | \(-30461917649505878016\) | \([]\) | \(7112448\) | \(2.4216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 348816.n have rank \(0\).
Complex multiplication
The elliptic curves in class 348816.n do not have complex multiplication.Modular form 348816.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
