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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 155610m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 155610.ff2 | 155610m1 | \([1, -1, 1, -124322, 16717821]\) | \(291498868418706649/3685655528100\) | \(2686842879984900\) | \([2]\) | \(1413120\) | \(1.7697\) | \(\Gamma_0(N)\)-optimal |
| 155610.ff1 | 155610m2 | \([1, -1, 1, -233672, -17049459]\) | \(1935594897227176249/946696265563230\) | \(690141577595594670\) | \([2]\) | \(2826240\) | \(2.1163\) |
Rank
sage: E.rank()
The elliptic curves in class 155610m have rank \(1\).
Complex multiplication
The elliptic curves in class 155610m do not have complex multiplication.Modular form 155610.2.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 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.
