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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 21780.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 21780.l1 | 21780n4 | \([0, 0, 0, -7732263, -8275761362]\) | \(154639330142416/33275\) | \(11001240747129600\) | \([2]\) | \(622080\) | \(2.4627\) | |
| 21780.l2 | 21780n3 | \([0, 0, 0, -484968, -128352323]\) | \(610462990336/8857805\) | \(183033142930368720\) | \([2]\) | \(311040\) | \(2.1161\) | |
| 21780.l3 | 21780n2 | \([0, 0, 0, -109263, -7855562]\) | \(436334416/171875\) | \(56824590636000000\) | \([2]\) | \(207360\) | \(1.9134\) | |
| 21780.l4 | 21780n1 | \([0, 0, 0, -49368, 4135417]\) | \(643956736/15125\) | \(312535248498000\) | \([2]\) | \(103680\) | \(1.5668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 21780.l have rank \(0\).
Complex multiplication
The elliptic curves in class 21780.l do not have complex multiplication.Modular form 21780.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
