Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2940.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2940.a1 | 2940c2 | \([0, -1, 0, -73516, 4878616]\) | \(4253563312/1476225\) | \(15250176894355200\) | \([2]\) | \(26880\) | \(1.8069\) | |
2940.a2 | 2940c1 | \([0, -1, 0, -30641, -1998534]\) | \(4927700992/151875\) | \(98059265010000\) | \([2]\) | \(13440\) | \(1.4603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2940.a have rank \(1\).
Complex multiplication
The elliptic curves in class 2940.a do not have complex multiplication.Modular form 2940.2.a.a
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.