Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 13872.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13872.w1 | 13872bn2 | \([0, 1, 0, -274357, 55251491]\) | \(-23100424192/14739\) | \(-1457207826395136\) | \([]\) | \(124416\) | \(1.8505\) | |
13872.w2 | 13872bn1 | \([0, 1, 0, 3083, 318371]\) | \(32768/459\) | \(-45380174524416\) | \([]\) | \(41472\) | \(1.3012\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13872.w have rank \(1\).
Complex multiplication
The elliptic curves in class 13872.w do not have complex multiplication.Modular form 13872.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.