Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 23275.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23275.l1 | 23275i3 | \([0, 1, 1, -942433, 351832919]\) | \(-50357871050752/19\) | \(-34927046875\) | \([]\) | \(122472\) | \(1.8111\) | |
23275.l2 | 23275i2 | \([0, 1, 1, -11433, 496794]\) | \(-89915392/6859\) | \(-12608663921875\) | \([]\) | \(40824\) | \(1.2618\) | |
23275.l3 | 23275i1 | \([0, 1, 1, 817, 669]\) | \(32768/19\) | \(-34927046875\) | \([]\) | \(13608\) | \(0.71250\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 23275.l have rank \(0\).
Complex multiplication
The elliptic curves in class 23275.l do not have complex multiplication.Modular form 23275.2.a.l
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.