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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 25152l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25152.bc4 | 25152l1 | \([0, 1, 0, -1889, 4095]\) | \(2845178713/1609728\) | \(421980536832\) | \([2]\) | \(27648\) | \(0.92066\) | \(\Gamma_0(N)\)-optimal |
| 25152.bc2 | 25152l2 | \([0, 1, 0, -22369, 1277951]\) | \(4722184089433/9884736\) | \(2591224233984\) | \([2, 2]\) | \(55296\) | \(1.2672\) | |
| 25152.bc3 | 25152l3 | \([0, 1, 0, -14689, 2176511]\) | \(-1337180541913/7067998104\) | \(-1852833294974976\) | \([2]\) | \(110592\) | \(1.6138\) | |
| 25152.bc1 | 25152l4 | \([0, 1, 0, -357729, 82233855]\) | \(19312898130234073/84888\) | \(22252879872\) | \([4]\) | \(110592\) | \(1.6138\) |
Rank
sage: E.rank()
The elliptic curves in class 25152l have rank \(0\).
Complex multiplication
The elliptic curves in class 25152l do not have complex multiplication.Modular form 25152.2.a.l
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.
