Show commands:
SageMath
E = EllipticCurve("fm1")
E.isogeny_class()
Elliptic curves in class 377520.fm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.fm1 | 377520fm2 | \([0, 1, 0, -31232986616, -2124567395990316]\) | \(464352938845529653759213009/2445173327025000\) | \(17742945093213126758400000\) | \([2]\) | \(464486400\) | \(4.4616\) | |
| 377520.fm2 | 377520fm1 | \([0, 1, 0, -1950986616, -33235243190316]\) | \(-113180217375258301213009/260161419375000000\) | \(-1887812912207439360000000000\) | \([2]\) | \(232243200\) | \(4.1150\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.fm have rank \(1\).
Complex multiplication
The elliptic curves in class 377520.fm do not have complex multiplication.Modular form 377520.2.a.fm
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.
