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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 116160.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.m1 | 116160i1 | \([0, -1, 0, -3320401, 2329880401]\) | \(104795188976/1875\) | \(72436153067520000\) | \([2]\) | \(2703360\) | \(2.3621\) | \(\Gamma_0(N)\)-optimal |
| 116160.m2 | 116160i2 | \([0, -1, 0, -3213921, 2486171745]\) | \(-23758298924/3515625\) | \(-543271148006400000000\) | \([2]\) | \(5406720\) | \(2.7086\) |
Rank
sage: E.rank()
The elliptic curves in class 116160.m have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.m do not have complex multiplication.Modular form 116160.2.a.m
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.
