Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 277200.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.a1 | 277200a2 | \([0, 0, 0, -2100583875, -41813580658750]\) | \(-878812616455788778465/138974375664304488\) | \(-162099711774844754803200000000\) | \([]\) | \(335923200\) | \(4.3332\) | |
| 277200.a2 | 277200a1 | \([0, 0, 0, 173896125, 210236701250]\) | \(498592699047570335/304907615857152\) | \(-355644243135782092800000000\) | \([]\) | \(111974400\) | \(3.7838\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.a have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.a do not have complex multiplication.Modular form 277200.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
