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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 172480.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172480.be1 | 172480ed4 | \([0, 1, 0, -1391665, 631438863]\) | \(154639330142416/33275\) | \(64139599462400\) | \([2]\) | \(1990656\) | \(2.0340\) | |
| 172480.be2 | 172480ed3 | \([0, 1, 0, -87285, 9771355]\) | \(610462990336/8857805\) | \(1067122586055680\) | \([2]\) | \(995328\) | \(1.6874\) | |
| 172480.be3 | 172480ed2 | \([0, 1, 0, -19665, 593263]\) | \(436334416/171875\) | \(331299584000000\) | \([2]\) | \(663552\) | \(1.4847\) | |
| 172480.be4 | 172480ed1 | \([0, 1, 0, -8885, -318725]\) | \(643956736/15125\) | \(1822147712000\) | \([2]\) | \(331776\) | \(1.1381\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 172480.be have rank \(2\).
Complex multiplication
The elliptic curves in class 172480.be do not have complex multiplication.Modular form 172480.2.a.be
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.
