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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 222180.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222180.e1 | 222180u1 | \([0, -1, 0, -5343605, -4752387978]\) | \(7124261256822784/475453125\) | \(1126146016595250000\) | \([2]\) | \(9123840\) | \(2.5194\) | \(\Gamma_0(N)\)-optimal |
| 222180.e2 | 222180u2 | \([0, -1, 0, -5012980, -5366424728]\) | \(-367624742361424/115740505125\) | \(-4386239633789038368000\) | \([2]\) | \(18247680\) | \(2.8659\) |
Rank
sage: E.rank()
The elliptic curves in class 222180.e have rank \(0\).
Complex multiplication
The elliptic curves in class 222180.e do not have complex multiplication.Modular form 222180.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
