Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 7245t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7245.h4 | 7245t1 | \([1, -1, 1, -212, -34]\) | \(1439069689/828345\) | \(603863505\) | \([4]\) | \(2816\) | \(0.37449\) | \(\Gamma_0(N)\)-optimal |
| 7245.h2 | 7245t2 | \([1, -1, 1, -2417, -45016]\) | \(2141202151369/5832225\) | \(4251692025\) | \([2, 2]\) | \(5632\) | \(0.72107\) | |
| 7245.h1 | 7245t3 | \([1, -1, 1, -38642, -2914036]\) | \(8753151307882969/65205\) | \(47534445\) | \([2]\) | \(11264\) | \(1.0676\) | |
| 7245.h3 | 7245t4 | \([1, -1, 1, -1472, -81304]\) | \(-483551781049/3672913125\) | \(-2677553668125\) | \([2]\) | \(11264\) | \(1.0676\) |
Rank
sage: E.rank()
The elliptic curves in class 7245t have rank \(0\).
Complex multiplication
The elliptic curves in class 7245t do not have complex multiplication.Modular form 7245.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
