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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3220.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3220.c1 | 3220c1 | \([0, 1, 0, -2632810, 1643408833]\) | \(-126142795384287538429696/9315359375\) | \(-149045750000\) | \([3]\) | \(35424\) | \(2.0402\) | \(\Gamma_0(N)\)-optimal |
| 3220.c2 | 3220c2 | \([0, 1, 0, -2606310, 1678138133]\) | \(-122372013839654770813696/5297595236711512175\) | \(-84761523787384194800\) | \([]\) | \(106272\) | \(2.5895\) |
Rank
sage: E.rank()
The elliptic curves in class 3220.c have rank \(0\).
Complex multiplication
The elliptic curves in class 3220.c do not have complex multiplication.Modular form 3220.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
