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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 138600bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138600.a4 | 138600bw1 | \([0, 0, 0, -9133050, -9421988875]\) | \(462278484549842944/57095309704125\) | \(10405620193576781250000\) | \([2]\) | \(8847360\) | \(2.9547\) | \(\Gamma_0(N)\)-optimal |
| 138600.a2 | 138600bw2 | \([0, 0, 0, -141488175, -647770756750]\) | \(107422839278466723664/2001871265625\) | \(5837456610562500000000\) | \([2, 2]\) | \(17694720\) | \(3.3012\) | |
| 138600.a3 | 138600bw3 | \([0, 0, 0, -136857675, -692144838250]\) | \(-24304331176056594436/3678122314453125\) | \(-42901618675781250000000000\) | \([2]\) | \(35389440\) | \(3.6478\) | |
| 138600.a1 | 138600bw4 | \([0, 0, 0, -2263800675, -41457717819250]\) | \(109999511474021786850916/38201625\) | \(445583754000000000\) | \([2]\) | \(35389440\) | \(3.6478\) |
Rank
sage: E.rank()
The elliptic curves in class 138600bw have rank \(1\).
Complex multiplication
The elliptic curves in class 138600bw do not have complex multiplication.Modular form 138600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
