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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 138600.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 138600.l1 | 138600ej3 | \([0, 0, 0, -19803675, 33920851750]\) | \(73639964854838596/9904125\) | \(115521714000000000\) | \([2]\) | \(5898240\) | \(2.6874\) | |
| 138600.l2 | 138600ej4 | \([0, 0, 0, -2280675, -484519250]\) | \(112477694831716/56396484375\) | \(657808593750000000000\) | \([2]\) | \(5898240\) | \(2.6874\) | |
| 138600.l3 | 138600ej2 | \([0, 0, 0, -1241175, 526914250]\) | \(72516235474384/833765625\) | \(2431260562500000000\) | \([2, 2]\) | \(2949120\) | \(2.3408\) | |
| 138600.l4 | 138600ej1 | \([0, 0, 0, -16050, 20937625]\) | \(-2508888064/1037680875\) | \(-189117339468750000\) | \([2]\) | \(1474560\) | \(1.9942\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 138600.l have rank \(0\).
Complex multiplication
The elliptic curves in class 138600.l do not have complex multiplication.Modular form 138600.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
