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SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 302016.ez
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 302016.ez1 | 302016ez2 | \([0, 1, 0, -1404729, -641100825]\) | \(42246001231552/14414517\) | \(104596259434647552\) | \([2]\) | \(4300800\) | \(2.2373\) | |
| 302016.ez2 | 302016ez1 | \([0, 1, 0, -75544, -12927994]\) | \(-420526439488/390971529\) | \(-44328314424753216\) | \([2]\) | \(2150400\) | \(1.8907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302016.ez have rank \(1\).
Complex multiplication
The elliptic curves in class 302016.ez do not have complex multiplication.Modular form 302016.2.a.ez
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
