Show commands:
SageMath
E = EllipticCurve("mw1")
E.isogeny_class()
Elliptic curves in class 310464mw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.mw2 | 310464mw1 | \([0, 0, 0, -8254764, -9138966480]\) | \(-35148950502093/46137344\) | \(-81654086445180125184\) | \([2]\) | \(11354112\) | \(2.7275\) | \(\Gamma_0(N)\)-optimal |
310464.mw1 | 310464mw2 | \([0, 0, 0, -132117804, -584507559888]\) | \(144106117295241933/247808\) | \(438571753367666688\) | \([2]\) | \(22708224\) | \(3.0741\) |
Rank
sage: E.rank()
The elliptic curves in class 310464mw have rank \(0\).
Complex multiplication
The elliptic curves in class 310464mw do not have complex multiplication.Modular form 310464.2.a.mw
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.