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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 224400.bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.bi1 | 224400ev2 | \([0, -1, 0, -57408, -3362688]\) | \(326940373369/112003650\) | \(7168233600000000\) | \([2]\) | \(1179648\) | \(1.7443\) | |
| 224400.bi2 | 224400ev1 | \([0, -1, 0, 10592, -370688]\) | \(2053225511/2098140\) | \(-134280960000000\) | \([2]\) | \(589824\) | \(1.3977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.bi have rank \(2\).
Complex multiplication
The elliptic curves in class 224400.bi do not have complex multiplication.Modular form 224400.2.a.bi
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.
