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SageMath
E = EllipticCurve("er1")
E.isogeny_class()
Elliptic curves in class 327600.er
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327600.er1 | 327600er1 | \([0, 0, 0, -3042675, 2042813250]\) | \(267080942160036/1990625\) | \(23218650000000000\) | \([2]\) | \(6881280\) | \(2.3163\) | \(\Gamma_0(N)\)-optimal |
| 327600.er2 | 327600er2 | \([0, 0, 0, -2979675, 2131454250]\) | \(-125415986034978/11552734375\) | \(-269502187500000000000\) | \([2]\) | \(13762560\) | \(2.6628\) |
Rank
sage: E.rank()
The elliptic curves in class 327600.er have rank \(0\).
Complex multiplication
The elliptic curves in class 327600.er do not have complex multiplication.Modular form 327600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
