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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 30960.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30960.t1 | 30960t2 | \([0, 0, 0, -1421523, 597112722]\) | \(3940344055317123/369800000000\) | \(29813855846400000000\) | \([2]\) | \(663552\) | \(2.4751\) | |
| 30960.t2 | 30960t1 | \([0, 0, 0, -315603, -57813102]\) | \(43121696645763/7045120000\) | \(567988621148160000\) | \([2]\) | \(331776\) | \(2.1285\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.t have rank \(1\).
Complex multiplication
The elliptic curves in class 30960.t do not have complex multiplication.Modular form 30960.2.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 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.
