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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 152880eb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.d2 | 152880eb1 | \([0, -1, 0, -261, -51960]\) | \(-1048576/621075\) | \(-1169101642800\) | \([2]\) | \(258048\) | \(0.99468\) | \(\Gamma_0(N)\)-optimal |
| 152880.d1 | 152880eb2 | \([0, -1, 0, -22556, -1282644]\) | \(42140629456/511875\) | \(15416724960000\) | \([2]\) | \(516096\) | \(1.3413\) |
Rank
sage: E.rank()
The elliptic curves in class 152880eb have rank \(1\).
Complex multiplication
The elliptic curves in class 152880eb do not have complex multiplication.Modular form 152880.2.a.eb
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.
