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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 93600bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.ey3 | 93600bw1 | \([0, 0, 0, -19425, -713000]\) | \(1111934656/342225\) | \(249482025000000\) | \([2, 2]\) | \(294912\) | \(1.4672\) | \(\Gamma_0(N)\)-optimal |
93600.ey4 | 93600bw2 | \([0, 0, 0, 53700, -4808000]\) | \(367061696/426465\) | \(-19897151040000000\) | \([2]\) | \(589824\) | \(1.8138\) | |
93600.ey2 | 93600bw3 | \([0, 0, 0, -120675, 15588250]\) | \(33324076232/1285245\) | \(7495548840000000\) | \([2]\) | \(589824\) | \(1.8138\) | |
93600.ey1 | 93600bw4 | \([0, 0, 0, -282675, -57838250]\) | \(428320044872/73125\) | \(426465000000000\) | \([2]\) | \(589824\) | \(1.8138\) |
Rank
sage: E.rank()
The elliptic curves in class 93600bw have rank \(1\).
Complex multiplication
The elliptic curves in class 93600bw do not have complex multiplication.Modular form 93600.2.a.bw
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.