Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 53361u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.cd2 | 53361u1 | \([0, 0, 1, -124509, 18375453]\) | \(-28672/3\) | \(-22335167517477507\) | \([]\) | \(470400\) | \(1.8761\) | \(\Gamma_0(N)\)-optimal |
53361.cd1 | 53361u2 | \([0, 0, 1, -48683019, -130846808997]\) | \(-1713910976512/1594323\) | \(-11869823760655763797587\) | \([]\) | \(6115200\) | \(3.1586\) |
Rank
sage: E.rank()
The elliptic curves in class 53361u have rank \(1\).
Complex multiplication
The elliptic curves in class 53361u do not have complex multiplication.Modular form 53361.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.