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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 194940.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 194940.e1 | 194940t1 | \([0, 0, 0, -233928, -43705548]\) | \(-5971968/25\) | \(-5926426084627200\) | \([]\) | \(1551312\) | \(1.8815\) | \(\Gamma_0(N)\)-optimal |
| 194940.e2 | 194940t2 | \([0, 0, 0, 545832, -230380092]\) | \(8429568/15625\) | \(-33336146726028000000\) | \([]\) | \(4653936\) | \(2.4308\) |
Rank
sage: E.rank()
The elliptic curves in class 194940.e have rank \(1\).
Complex multiplication
The elliptic curves in class 194940.e do not have complex multiplication.Modular form 194940.2.a.e
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
