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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 334620.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
334620.be1 | 334620be4 | \([0, 0, 0, -2367183, 761493382]\) | \(1628514404944/664335375\) | \(598432244734168416000\) | \([2]\) | \(14929920\) | \(2.6844\) | |
334620.be2 | 334620be2 | \([0, 0, 0, -1089543, -437699522]\) | \(158792223184/16335\) | \(14714541909999360\) | \([2]\) | \(4976640\) | \(2.1351\) | |
334620.be3 | 334620be1 | \([0, 0, 0, -62868, -7933367]\) | \(-488095744/200475\) | \(-11286722487783600\) | \([2]\) | \(2488320\) | \(1.7885\) | \(\Gamma_0(N)\)-optimal |
334620.be4 | 334620be3 | \([0, 0, 0, 484692, 86739757]\) | \(223673040896/187171875\) | \(-10537757878254750000\) | \([2]\) | \(7464960\) | \(2.3378\) |
Rank
sage: E.rank()
The elliptic curves in class 334620.be have rank \(1\).
Complex multiplication
The elliptic curves in class 334620.be do not have complex multiplication.Modular form 334620.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.