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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 68970l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68970.o1 | 68970l1 | \([1, 1, 0, -444677, 58713549]\) | \(5489125095409201/2330634240000\) | \(4128860724848640000\) | \([2]\) | \(1935360\) | \(2.2687\) | \(\Gamma_0(N)\)-optimal |
| 68970.o2 | 68970l2 | \([1, 1, 0, 1491323, 434684749]\) | \(207053365326094799/165767088643200\) | \(-293666509323836035200\) | \([2]\) | \(3870720\) | \(2.6153\) |
Rank
sage: E.rank()
The elliptic curves in class 68970l have rank \(1\).
Complex multiplication
The elliptic curves in class 68970l do not have complex multiplication.Modular form 68970.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
