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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 11616m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11616.s3 | 11616m1 | \([0, 1, 0, -4154, -91104]\) | \(69934528/9801\) | \(1111236439104\) | \([2, 2]\) | \(15360\) | \(1.0376\) | \(\Gamma_0(N)\)-optimal |
| 11616.s1 | 11616m2 | \([0, 1, 0, -64049, -6260289]\) | \(4004529472/99\) | \(718375071744\) | \([2]\) | \(30720\) | \(1.3842\) | |
| 11616.s2 | 11616m3 | \([0, 1, 0, -17464, 792680]\) | \(649461896/72171\) | \(65461928412672\) | \([4]\) | \(30720\) | \(1.3842\) | |
| 11616.s4 | 11616m4 | \([0, 1, 0, 6736, -478788]\) | \(37259704/131769\) | \(-119519652561408\) | \([2]\) | \(30720\) | \(1.3842\) |
Rank
sage: E.rank()
The elliptic curves in class 11616m have rank \(1\).
Complex multiplication
The elliptic curves in class 11616m do not have complex multiplication.Modular form 11616.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
