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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 69696.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69696.er1 | 69696fu2 | \([0, 0, 0, -175692, 110803088]\) | \(-121\) | \(-4956719031026712576\) | \([]\) | \(811008\) | \(2.2700\) | |
| 69696.er2 | 69696fu1 | \([0, 0, 0, -17292, -875248]\) | \(-24729001\) | \(-23123460096\) | \([]\) | \(73728\) | \(1.0711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 69696.er have rank \(0\).
Complex multiplication
The elliptic curves in class 69696.er do not have complex multiplication.Modular form 69696.2.a.er
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
